So at the end of the day, to check that a real-valued function is measurable, by definition we must check that the preimage of a Borel measurable set is measurable.

Jul 3, 2020 · measurable functions provides a mathematics framework for what one would call "observables" in science (other than Mathematics, that is). The definition you presented, …

Jan 4, 2022 · Let's think about definitions. For a function to be measurable, the inverse image of open sets must be measurable. What is the domain of a measure? The domain is a sigma …

I always see this word F F -measurable, but really don't understand the meaning. I am not able to visualize the meaning of it. Need some guidance on this. Don't really understand σ(Y) σ (Y) …

There is no definition of "measurable set". There are definitions of a measurable subset of a set endowed with some structure. Depending on the structure we have, different definitions of …

Closure, Interior, and Boundary of Jordan Measurable Sets. Ask Question Asked 13 years, 2 months ago Modified 10 years ago

The only explanation I've ever seen is that a set is measurable if it 'breaks up' other sets in the way you'd want. I don't really see why this is the motivation though. One reason I am not …

Oct 9, 2024 · As the actual product measurable space is the smallest, it can only be smaller, hence the diagonal is definitely not part of the actual product measurable space either. I …

Jun 16, 2015 · I need help to prove the following theorem Suppose f f is the pointwise limit of a sequence of fn f n, n = 1, 2, ⋯ n = 1, 2,, where fn f n is a Borel measurable function on X X. …

Mar 21, 2024 · However, the sigma-algebra in general is a larger than the topology, so is there any chance that a map that brings measurable sets to measurables sets is a measurable map ?