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 attachment where, e.g., a pre-structure is a sequence of sets whose union equals A and each term of the sequence has a positive uniform probability measure; how do we answer the following question in section 2?
Does there exist a unique extension (or method constructively defining a unique extension) of the expected value of f when the value’s finite, using the uniform probability measure on sets measurable in the Caratheodory sense, such we replace f with infinite or undefined expected values with f defined on a chosen pre-structure depending on A where:
How do we answer this question?
(See sections 3.1 & 3.3 in the attachment for an idea of what an answer would look like)
Edit: Made changes to section 3.5 (b) since it was nearly impossible to read. Hopefully, the new version is much easier to process.
This appears to be a thesis or at least a advanced exam problem. I suggest you consult your advisor. David Booth
You’re right; however, my advisor Markus Pomper is too busy to answer and I can’t ask the question on math stack exchange as it doesn’t have enough focus.
I’m currently in contact with a statistician from varsity tutors; however, from previous sessions it appears he doesn‘t have enough knowledge to answer all doubts in the attachment.
I’m also in contact with a Phd student from Italy; however, he responds only once every Sunday. (He states once he gets time he will give a proper response.) This could take a couple of months in which I’m currently away from college (to avoid failure due to obsession with research) the only options buy time is to get a job, exercise or watch videos. (The last time I had a job it didn’t end on good terms as managers are very strict with time.)
Finding someone with the knowledge and time to tackle the main question (and remaining questions in the attachment) are extremely challenging. I must make sure the attachment is understandable to experts. (Note there are several new definitions which require better alternatives.)
Let me know if you there is someone with the knowledge and time to answer my doubts.
Btw, I‘m undergrad. I think the question is too complicated for an undergrad thesis.
Einstein was also determined to answer questions he found worth pursuing, so, continue studying , reading, writing, and , sharpen your mind by studying published refereed papers as well, and then, after maybe quite some time, you really know, whether what you are doing is really worthwhile , and then, knock on the door of a professor.....and YOU should tackle your questions......and, also very important, when you write a research paper, introduce your problem carefully, in such a way, that your paper triggers the minds of those, who are reading your paper, and, do not write , in the beginning , in a terse style.
Good luck, and take your time, as did Einstein and Gödel or Hilbert!
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