What should be used to instead of '='mean equal in the order, /numerically equal in value for non numerically identical events in order theory?

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...

09 October 2017 2,817 0 View

Is the 2 canonical probability simplex (triples)uniquely represented by a vector probability function ranked point-wise,/numerically by tself ?

Ie where the function is non negative and bounded 0

09 October 2017 7,775 1 View

Difference between an order automorphism and order isomoprhism?

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...

09 October 2017 5,943 16 View

Do strong qualitative probabilistic representations over finite sets constitute order isomorphisms when not unique or an order emebdding without =?

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

09 October 2017 1,949 0 View

Are there counter-examples to strong representability by a merely normalized probability like function? (only closed singletons , unit,0?

08 September 2017 1,034 0 View

Is the Canonical unit 2 standard probability simplex closed under all and only convex combinations of two values and which sum to any value in (0,1)?

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...

07 August 2017 4,162 2 View

State dependenent additivity and state indenpendent additivity ; akin to the cauchy kolmorgov additivity distinction?

07 August 2017 8,292 1 View

Midpoint convex monotone increasing F on closed interval rationally convex? linear with three fixed pts

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...

06 July 2017 1,067 0 View

Are these two pieces of notations equivalent

06 July 2017 4,258 1 View

F:[0,1]to[0,1]Functional equation,ifF(x)+F(y)=1\F(x)+F(y)+F(z)=1,cauchy's equation over the unit triangle with F(1)=1 i

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...

05 June 2017 9,884 1 View