Bharath Krishnan

13 Questions 13 Answers 0 Followers

Questions related from Bharath Krishnan

How do we define a unique, satisfying expected value from chosen sequences of bounded functions converging to an everywhere surjective function?

Consider an everywhere surjective function whose graph has zero Hausdorff measure in its dimension. See this link for more details: https://matchmaticians.com/questions/cygsg6 I will pay $100...

03 March 2025 7,621 2 View

Is there a more non-uniform set with positive measure in any rectangle of the plane, where the measures don't equal the area of the rectangles?

(If you don't need the motivation, skip it. Note, [1]-[4] are citations for links at the bottom of this post.) Motivation: I want to find a set A⊆ℝ2 which is more non-uniform [1] and difficult to...

07 September 2024 7,259 0 View

Is there a name for this type of function?

Let n∈ℕ, where the function f:A⊆ℝ𝑛→ℝ, 𝐴 is Borel, and (A,d) is a completely seperable space. What is the name of the functions where the graph of f in any (n+1)-dimensional box of A×ℝ is...

18 July 2024 476 1 View

Is the following regarding an everywhere, surjective function true?

Suppose: For natural number n, set A⊆Rn, set B⊆R, and (A,P) is a Polish Space (i.e., a space homeomorphic to a complete metric space that has a countable dense subset.) An everywhere surjective...

28 March 2024 688 3 View

Does there exist a explicit, bijective function f:R→R whose graph is dense in R x R?

Does there exist a explicit, bijective function f:R→R where the graph of f is dense in R x R?

21 January 2024 7,760 2 View

Does the set of unbounded sets, where the mean of the sets is finite, have a cardinality less than the cardinality of all unbounded sets?

Let n ∈ N where set A ⊆ Rn. Suppose a set A is unbounded, if for any r>0 and x0 ∈ Rn, d(x,x0)>r for some x ∈ A, where d is the standard Euclidean Metric of Rn. If U is the set of all unbounded A...

04 September 2023 3,248 9 View

Finding a choice function which chooses a unique set of equivalent sequences of sets, where the expected value is unique, natural and finite?

(See attached article for more info). Let (X,d) be a metric space. If set A⊆X, let Hα be the α-dimensional Hausdorff measure on A, where α∈[0,+∞) and dimH(A) is the Hausdorff measure of set...

03 July 2023 834 1 View

Is there a simpler measure for the uniformity of measurable subsets of [0,1] x [0,1]?

In the attatchment below, I defined a new measure between 0 and 1 that measures the uniformity of subset R of [0,1] x [0,1] w.r.t a set that's "uniform" in [0,1] x [0,1] with Hausdorff dimension d...

09 June 2023 5,179 0 View

Does the following function exist?

Does there exist a function f:[0,1]->[0,1] such the function f is measurable in the sense of caratheodory the graph of f is dense in [0,1] x [0,1] the collection of all subsets of the range of...

15 May 2023 2,123 0 View

Finding expected value of uncountable pseudo-random points, non-uniformly distributed over the sub-space of R^2?

Consider the following...

12 April 2023 9,187 0 View

The most generalized, natural extension of the expected value?

Suppose A is a set measurable in the Caratheodory sense such for n in the integers, A is a subset of Rn, and function f:A->R After reading the preliminary definitions in section 1.2 of the...

02 March 2023 8,694 3 View

Is the set of all measurable functions with infinite or undefined expected values a prevelant subset of the set of all measurable functions?

When a set of functions with a property is a prevalent subset of some other set of functions, almost all functions with that property belong to that set of functions. Is it true the set of all...

02 March 2023 8,558 5 View

How do we find a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Caratheodory with no gauge func.?

Edit: I updated question 1 and added a link in Section 3.1. I also explained the intuition in section 4.4.1. I have yet to understand amenability and group theory, but the questions in my...

01 June 2022 5,867 1 View