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Questions related from William Balthes
Is there any difference between an order iso-morphism (often defined as a -bi-jective (or sur-jective ) order embedding and an order auto-morph-ism in the context of the same numerical domain of...
10 October 2017 6,063 16 View
Ie where the function is non negative and bounded 0
10 October 2017 7,904 1 View
Suppose one has a numerical order (objective probability) that is to be represented by another numerical order F (subjective probability) .Where the events are ordered pointwise numerically. W...
10 October 2017 2,941 0 View
When a complete comparative qualitative probability order defined over a finite but complete power algebras that is complete in the order. \forall events in P(\omega): A
10 October 2017 2,069 0 View
It is well known that for a total qualitative probability order 〈 S, F=𝒫 (S), ⪋ 〉↦ S, F=𝒫 (S),P〉 Scotts axiom's, in addition to (1), (2), (3) tothe axioms of non negativity : (1)∀ (A_i)∈ F:...
09 September 2017 1,148 0 View
Is the canonical unit 2 standard probability simplex, the convex hull of the equilateral triangle in the three dimensional Cartesian plane whose vertices are (1,0,0) , (0,1,0) and (0,0,1) in...
08 August 2017 4,309 2 View
State dependent additivity and state independent additivity? ; akin to more to cauchy additivity versus local kolmorgov additivity/normalization of subjective credence/utility, in a simplex...
08 August 2017 8,455 1 View
presume that midpoint convex F: [0,1] to [0,1] is monotone increasing (not necessarily strictly ) F(0)=0 ,F(0.5)=0.5 F(1)=1 , As its monotone increasing and midpoint convex with F(0)=0 F(1)=1 it...
07 July 2017 1,210 0 View
is the notation,'≧' equivalent to ≥ ,likewise,are tfor greater then or equal to, at least in the context of analysis or order theory is notation for super ⫆ equivalent to ⊇ .? I am seen this use...
07 July 2017 4,412 1 View
Is the following function F:[0,1] to [0,1] F strictly monotonic increasing F(1)=1,(i presume this unnecessary as its specified by the first two (1)ie x+y=1 if and only iof F(x)+F(y)=1...
06 June 2017 10,022 1 View
Am i correct in presuming that probability function satisfying point reflection symmetry at all points would be linear, ie F-1(x)=F(x); where F(x) is a bi-jective strictly increasing function...
04 April 2017 3,564 0 View
Does anyone know of the technical (functional equations) conditions that are required for a function to satisfy mirror/reflection/square symmetry or square symmetry let alone point reflection...
04 April 2017 7,040 1 View
I have seen this condition being used for midpoint convexity: Midpoint convexity. A set C is midpoint convex if whenever two points a,b are in C, the average or midpoint (a + b) is in c.; I have...
04 April 2017 2,443 1 View
I was wondering if there are any set of n; n>=3continuous or somewhat smooth functions (certain polynomials), all of which have the same domain [0,1] f^n(min,max):[0,1] \to[min,max]; where...
02 February 2017 2,561 5 View
What are the distinctions between 1. Continuity,https://en.wikipedia.org/wiki/Continuous_function#Continuous_functions_between_topological_spaces And also first part of rao and rao...
02 February 2017 6,809 8 View
See attached this lemma 3 and the last part of the proof above lemma 3, which is the inequality 'which suffices for this claim' which then proceeds to lemma 3; in this inequality methods, where...
01 January 2017 1,270 8 View
Is there a distinction between a qualitative /comparative probabilistic structure, ie which admits of a 1. strong numerical probabilistic representation and said representation is unique (given...
01 January 2017 9,124 2 View
See Fellow As I suggested in a previous questions, is it merely the case that all of these stronger probability to limiting relative frequency theorems, are only stronger in the sense, (A) not...
01 January 2017 2,111 2 View
I wonder if it would be interesting if anybody had ever thought of whether there was any reason behind born denoting the quantum probability rules as given only by the moduli of the amplitude as...
12 December 2016 1,482 0 View
Barnum (2003) references the following paper by Ruttiman 1. , inverted commas, " " I have attached the barnum paper as well. Does anyone know whether the Ruttimann paper below;references was...
11 November 2016 3,429 8 View
Is there any connection between the eigenvalues of spin up and spin down of particles that is measured in x versus the -x direction?. Ie if we instead decide the measure the basis of the same...
11 November 2016 4,235 0 View
Is it plausible that the contextuality of meausurements outcomes within distinct contexts is somewhat responsible for the fact that a quantity entity cannot be in two non-orthogonal but...
11 November 2016 1,177 0 View
Can a long run frequentist even use, let alone make sense of kolmogorov's generalization of the strong law of large numbers for non identically distributed independent events (where relative...
11 November 2016 3,064 1 View
Has anyone ever considered the notion (not that i endorse it) that the appearance of a difference in temporal ordering reference frames; is rather a distinction between the different outcomes of...
11 November 2016 5,844 15 View
Has anyone ever met the constraint of scotts infinite theorem; is proof by contradiction the methodology by which its constrains can be shown to hold. Ie can presumably cannot so much as use proof...
11 November 2016 2,353 5 View
Do degrees of entanglement just measure different kinds of correlations or different kinds of entangled states. I presume that maximally entangled state are more likely to engender deterministic...
11 November 2016 757 0 View
mples of models that have satisfied scotts infinite representation (probability)theorem? Does it make some kind of archimedean assumption or does that need to be assumed to meet said constraints;...
11 November 2016 3,271 2 View
GIven that the projection postulate (i believe) and/or the collapse postulate are often considered additions to the quantum formalism; is the notion of a preferred basis, the basis upon which a...
11 November 2016 1,993 13 View
I remember reading C. Piron suggesting (in a paper) that his two compatible complement (or orthocomplented) questions corresponding to a questions 'is it 'spin up' 'such that spin up would be the...
11 November 2016 7,390 1 View
1.Have systems involving say spin 1/2 particles even been implemented which verify or would exhibit the contextual characteristics of the three box paradox and or spectors parable of the seer,...
11 November 2016 7,942 1 View
In order to single out the contexts under which two quantum observables are considered to have the same probability for spin up and or spin down, such that non-contextuality of probabilities...
11 November 2016 2,743 4 View
Am I correct in saying that a hyper-finite frequentist account of probability would require not just absolute convergence of relative frequencies in the absolute limit but an absolute arithmetic...
11 November 2016 307 1 View
Has it even been proposed that just as evettianism claims to solve the measurement problem (of orthogonal outcomes) by having both outcomes occurring in a different world, that likewise the wave...
11 November 2016 10,000 6 View
If the agents are considered free in their betting behaviour within the confines of the decision theoretical proofs of the born rule in everettianism; would this not be also analyzed (under their...
11 November 2016 4,659 1 View
Mackysinki , and others (see wilce in stanford encylopedia) define two events to A and B to be equivalent iff P(A), s)=P(B,s) for all states.it is callsed: "outcome-separating" (see Four and a...
11 November 2016 5,600 2 View
Are there any analog's of villegas atomless constraint to provide a unique probability representation for finite systems, by embedding infinitely many finite systems together (as if they are...
11 November 2016 10,025 1 View
Is there any basis way to calculate when identically prepared and measured particles will exhibit a form anti-correlation due to maximal entanglement. By this I mean an anti-correlation; i need to...
11 November 2016 9,232 3 View
Is detector setting dependence (as opposed to apparatus parameter or measurement setting dependence) as used by Horward Wiseman (among others), a code word for a dependence between contexts, or on...
11 November 2016 9,872 5 View
Does anybody know of any examples in the literature; or otherwise whether it is possible to prove that a certain probabilistic logic satisfies the qualitative constraints given by Luce 1967 (the...
07 July 2016 1,834 1 View
Does anyone have an electronic copy of, or know where or how to find an electronic copy of the article: FENSTADJ,. E., 'A limit theorem in polyadic probabilities', Proc. Logic Colloquium 1965...
06 June 2016 4,662 2 View
I was wondering if anybody knows of a probability model that sketchs or outlines a proof of finite cancellation or general finite cancellation axioms (in relatively explicit detail), in order to...
06 June 2016 5,765 1 View
I tend to get conflicting answers as to whether 2^countable gives an answer that is of countable or uncountable cardinality It technically depends on ordinal versus cardinal...
06 June 2016 2,265 8 View
This is the basic idea, we imagine the chance set up in our world, say a coin that is flipped, which has some chance for the outcome A, where A here could be 'the coin lands heads up'. Lets say...
06 June 2016 568 11 View
In Von Neumann's later unpublished worked, he suggested that the logical structure alone (by that i mean the 'if then' relations of quantum logic) gives us the quantum probability calculus, and...
05 May 2016 4,280 9 View
I was wondering whether there has been any investigation into the distribution of the decimals of pi using nonstandard analysis. For instance can it proven that the frequency distribution is...
05 May 2016 1,580 3 View
Let me rephrase this. My central question is what is de finetti's theorem as opposed to the convergence result and which convergence result is deemed the central de finettis law of large number...
05 May 2016 1,078 1 View
Do people know where to find the works of ALEXANDER IACOVLEVICH KHINCHIN, especially his 1937 papers. Apparently he works on a frequentist account of probability that did not make use or require...
05 May 2016 5,473 6 View
This questions is part of a line of questions that point at the distinction between quantum and classical probability theory Did Kolmogorov actually propose a model theory for his calculus from...
05 May 2016 8,779 8 View
Given that there are still attempts to prove borns rule in other ways I get the impression that there must be something other than the mere structure of the logic which requires that probabilities...
05 May 2016 363 0 View
I was wondering if anyone has come up across the terminology "exact strong law of large numbers'. These appear to be stronger convergence theorems relating probability to (limiting- an abuse of...
04 April 2016 8,285 10 View
I have a question concerning subjective bayesianism. Even If a bayesian uses conditionalization and baye's rule to update their credence distributions, in what sense can they actually interpret...
04 April 2016 2,335 0 View
Scotts theorem and other theorems give conditions under which a qualitative ordering (>= for at least as probable than) which satisfies certain constraints (total pre-order, finite cancellation...
04 April 2016 5,653 1 View
what does this it mean for a real valued function F([A,B])=[C,D], B>D,A>B ? [C.D]\subset R where F is a function whose domain is [A,B]? ie [0,1] for example> Does this mean F's image...
01 January 1970 3,533 0 View
Perhaps I am not thinking straight, or I might have to use a some multidimensional mapping. But consider two mutually exhaustive variables A, B such they have a 'probability' m (for A), y...
01 January 1970 3,502 1 View
The only uniformly (equi-continuous, at least) functions that satisfy these constraints? These are probability functions, roughly such that are, which are 1.The domains equal the range...
01 January 1970 9,080 3 View
I attempted to explain in convoluted terms, a question I had before. The questions concerns, whether, there the cauchy field equation 1.F(xy)=F(x)F(y) and 2.F(x+y)=F(x)+F(y) with 3. F:[0,1]to...
01 January 1970 10,079 2 View
Iis there any discrete analogue m of star convexity at 0' star convexity at 0',? That is, in the same way that midpoint convexity can be seen to be a discrete analogue of convexity (and entails...
01 January 1970 5,847 2 View
What if any are the benefits, of presuming or deriving that a function:F :F:[0,1] → [0,1] . F being a tandard real valued function of one argument, -not a partial function, that assigns exactly...
01 January 1970 3,050 2 View
Let F1,F2 be two increasing functions on [a,b] and F1(x)=F2(x) on a dense subset of [a,b] and F2 is continuous. Then F1=F2 on and is continuous (a,b).? In my case F:[0,1] to [0,1] and F agrees...
01 January 1970 4,205 15 View
Suppose (1)F:[0,1]to[0,1] (2)F(1)=1 (3)and \for all (x,y)\in dom(F)=[0,1];F(x+y)=F(x)+F(y) then continuity is automatic, F(x)=x, without even assuming mono-tonicity, much less continuity due to...
01 January 1970 994 11 View
I have been told that one can, in some sense construct line like entities, for which have more then two 'end points' such as splines/polylines and other multi-dimensional or odd entities. Although...
01 January 1970 3,014 2 View
Are there sets of three, or rather for any N>3 sets of N sur-jective uniformly continuous functions, for all N>3, where n denotes the number of function in the sets, such that each...
01 January 1970 9,780 11 View
What is the name for the identities (2) and (3) in the functional analysis literature F-1(is the inverse function? where (1) F:[0,1] to [0,1] and F is strictly monotonic increasing where F(0)=0,...
01 January 1970 933 32 View
F strictly monotone increasing function Let F:[0,1] to [0,1] ; (1)Let F be midpoint convex only at 1, and 0 F(x/2)
01 January 1970 8,498 1 View
Consider the following 2 bijective function F:[0,1] to [0,1] where (1) F strictly increasing, and absolutely continuous function on [0,1] and and satisfies (2)), (3) and (4) (2) F(0)=0, with...
01 January 1970 9,801 6 View
Is there any special significance to the term 'Real valued function" other than the fact that said function in a the standard numerical sense that assignes to real numbers from the dom F:R\to R, a...
01 January 1970 6,860 12 View
Consider a continuous and convex function (not necessarily presumed to be differentiable that is such that F:[0,1]\to [0,1] F is continuous and convex F(0)
01 January 1970 8,747 27 View
J Ascel (1965, p241,246,196 ,281,286): in his' lectures on Functional equations and their applications)' pictures attached on page (196) Azcel, Describes a condition for a real valued function...
01 January 1970 9,992 5 View
- Can a Continuous, and (twice differentiable)Strictly (monotone)Increasing Function F. F:[0,1] to [0,1]; F(1)=1 F(0)=0, F(0.5). 1.can F both strictly pseudo-concave and strictly pseudo...
01 January 1970 2,657 9 View
Is a function that is Strictly montonely increasing and Uniformly Continuous, with positive first derivative; and thrice differentiable F:[0,1] to [0,1]. F(0)=0, F(1)=1, F(0.5)=0.5 is F alwas...
01 January 1970 345 6 View
What exactly are order embeddings.? Of the form x
01 January 1970 9,461 3 View
Are there any examples of absolutely continuous, strictly monotonic increasing functions that bijections of the unit interval to the unit interval,F:[0,1] to [0,1],that are doubling functions :...
01 January 1970 3,117 12 View
Does anyone know if an english versionPersonelle und Statistische WahrscheinlichkeitPersonelle Wahrscheinlichkeit und Rationale Entscheidung; in particular the second half called Stegmiiller, W.,...
01 January 1970 9,115 1 View
What is generally meant by this requirement, A set of states must be a partition of the proposition space that is orthogonal to the act partition??? It appears to be often a prerequisite of...
01 January 1970 8,506 0 View
Is it just me or is it the case, that not everyone seems to realize that dominance reasoning (at least of actual utilities as opposed to generalized dominance of expected values, but even there...
01 January 1970 7,460 3 View
I am wondering whether any mathematical packages (i presume that there are) such as matlab, or mathematica, have the facilit/ies to prove whether or rather derive what a certain sequence converges...
01 January 1970 8,190 0 View
Does anyone know where I can find or purchase these works in the particular the first reference "Some aspects of functional equations," 1979 J. Dhombres,which is relatively well cited in Azcel...
01 January 1970 4,259 1 View
Does anyone know if there are english translations available of these two works (and perhaps other publications ) of C Piron: 1.Axiomatique quantique 1964, Helvetica Physica Acta 37 2 Piron 1990;...
01 January 1970 8,251 4 View
When it was shown that de finetti's conjectures was false, by way of Krafts M=5 example; by which I mean that all finite qualitative orderings which meet his conditions are representatbe even if...
01 January 1970 3,819 4 View
Does there exist uniqueness ( of representation) theorems for dempster schafer and or other weaker formalisms of which the probability measure is a subclass? (presumably it would have to be at...
01 January 1970 3,381 0 View
Does anybody know of any derivation of Scotts general axiom (proven in zolton domotor's 1969 phd thesis), say within a probabilistic logic of some sort, which provides sufficient and necessary...
01 January 1970 7,094 1 View
Is there a distinction between strong or complete qualitative probability orders which are considered to be strong representation or total probability relations neither of which involve in-com...
01 January 1970 7,093 2 View
. .This regard the orthogonal additivity functional equation 1. Does $z\bot m$ denote events mean events whose amplitude modul-i squared $(P(A), PR(B)) = (z, m)$ which are disjoint, and can be...
01 January 1970 8,067 5 View
What is general, is meant by the orthogonality relation x⊥y in the functional equation: orthogonal additivity below (1) (1)∀(x,y)∈(dom(F)∩[x⊥y]):F(x+y)=F(x)+F(y) Particularly as used in the...
01 January 1970 1,327 3 View
What exactly is separability or countable order - density - as opposed to density as in a dense or bottom-less total order. particularly with regard to probabilistic representations? I know that...
01 January 1970 4,561 4 View
Is there exist at least 9 distinct a bi-j-ective, diffeomorphic& homoeomorphic. analytic functions F(x,y), dom i of two variables in the x,y, cartesian plane F(x,y); dom...
01 January 1970 4,313 28 View
Is there a general name for these 'pair' of symmetic probability functional equations (1) and (2); see https://math.stackexchange.com/posts/2239756/edit 1. F(1-x)+F(x)=1 = F(1)=F-1(1) 2....
01 January 1970 4,166 13 View
With regard to Jensens equality (before continuity is applied) where F(0)=0 and (and F(1)=1 if need be, which is not required ); Jensen's equation beingF(x+y)/2=F(x)/2 +F(y)/2 Is this literally...
01 January 1970 5,733 8 View
See attached document page 14; the equation expressed by sublinear functions when convex. Do they mean midpoint convexity here?. Likwise am i correct taht 2F(x)=f(2x) is not usually a property of...
01 January 1970 1,800 4 View
Where F:[0,1] to [0,1] (forall x,y z,m)\in dom (F)=[0,1] x+y=z+m, iff F(x)+F(y)=F(z)+F(m) This is the identity, am I correct that this is roughly equivalent to Jensen's equality over the...
01 January 1970 7,993 4 View
what does this it meant for a frame function to be self ad-joint or regular for instance Is this some kind of bijective involution roughly; can it in non quantum terms be read as equal to its own...
01 January 1970 7,322 2 View
In quantum mechanics, there are at least two main categories of measurement outcome/truth value contextuality. Kinds of contextuality 1. environmental 2. algebraic However I have also come...
01 January 1970 7,888 0 View
Does anybody know if Robin Giles is contact-able or is still active in research. By Robin Giles I mean the physicist who developed the Giles games dia-logial/game theoretical semantics and the...
01 January 1970 1,349 2 View
I sometimes see attempts at deriving the born rule, 'or what i call the quantum principal principle' which make an empirical assumption (no signalling) to justify what appears to an...
01 January 1970 8,014 3 View
hat exactly is the experimental difference in applying the projection operator P to a spin 1/2 x system from that of its ortho-complement (i think that is the word) 1-P (1 being the identity...
01 January 1970 8,088 2 View
Does anyone know the general continuous functional form of these constraints. Given, Midpoint convexity, it appears to satisfy jensen equality; symmetry appears to give one the other half....
01 January 1970 4,767 1 View
if F is strictly montone increasing function F:[0,1] such that F(0)=0 and F(1)=1 and satisfies jensens equation at x=0 and at x=1 ie the restricted form where F([1+x])=F(1)/2+F(x)/2 and...
01 January 1970 2,634 1 View
if F is a real valued injective functionF: F:[0,1] to [0,1] 1. F is midpoint convex 2. F is strictly monotone increasing 3. F(0)=0 and F(1)=1 Is F convex and continuous.? See attached article...
01 January 1970 8,736 7 View
Is there any mainstream or conventional view of what 'orthogonality' denotes for the functional equation, 'orthogonal additivity'. Correct me if I am wrong but the only bases or rather events,...
01 January 1970 2,106 23 View
Sub-linear functions over the real line. Are these equivalent to linear functions, when continuous and F(0)=0? Sublinear F often satisy sub-additivity (A) and a form of Homogeneity...
01 January 1970 3,926 4 View
I note that villegas condition (with monotone continuity) given a total ordering and the other general axioms of qualitative probability are sufficient for a unique strong representation. However...
01 January 1970 4,622 1 View
Suppose I have multiple distinct and disjoint and mutually exclusive sample space, either actual or hypothetical. Where each space is individually finitely representable for instance, but where...
01 January 1970 3,474 1 View
The paper attached below on page 35 says: ...."Kolmogorov existence of the stochastic process describing all P(A) in a coupled way subjects these to consistency the requirements expressing that...
01 January 1970 7,485 0 View
I was wondering if someone knows whether Mathematica allows one to plot another 'probability function over the unit 2 simplex (it can be expressed as a function of two arguments subject to...
01 January 1970 5,465 4 View
Does quiggin's and chew logarithmic function satisfy the properties in my question, earlier. If so would want to avoid it. See page 59 and 60 in See page 59 and 60 of Quiggin's, rank dependent...
01 January 1970 9,569 0 View
Is there a distinction between strong representations and the unique-ness properties that strong representations of probability representations of (1)type P\leq Q iff Pr(Q)\leq PR(M) often under...
01 January 1970 2,699 3 View
Is the ortho-complement of a proposition, in quantum logic/probability or hilbert space, the logical comple-ment of a proposition such as 'spin up at direction x and 'spin down in direction...
01 January 1970 3,565 2 View
What the name of this functional(A) equation for F:[0,1] to [0,1] (A) F(1-(x+y)=1-F(x)-F(y) Name of this functional equation? it specifies F(1/3)=1/3 and this (B)...
01 January 1970 2,848 8 View
are midpoint convex functions F(x/2+y/2)=F(x)+F(y); for pairs of points or rational numbers (or something...
01 January 1970 7,721 11 View
https://math.stackexchange.com/questions/2265396/can-this-strictly-increasing-convex-function-f-meet-its-linear-line-segment-in three places. See my post Is this correct that this result or...
01 January 1970 4,862 1 View
I am wondering whether there are some weaker forms of midpoint convexity; in my system it appears that jensens equation, as far as I can see, will just fall out; if not cauchy equation or...
01 January 1970 6,857 2 View
And are there some stronger forms of contextuality then independent state contextuality or algebraic/ontic/measurement contextuality, Where I use stronger meaning, smaller differences in context,...
01 January 1970 9,549 2 View
