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 …

It is not true, in general, that the inverse image of a Lebesgue measurable (but not Borel) set under a continuous function must be Lebesgue measurable. The definition of a 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, …

I always see this word 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) …

Mar 21, 2019 · Counterexample: let A A be any non-measurable set in R R and E = A × {0} E = A × {0}. Then E E is Lebesgue measurable but its first projection is not.

Jan 18, 2021 · What is "progressive" about progressively measurable processes? Ask Question Asked 4 years, 5 months ago Modified 2 years, 8 months ago

Jul 29, 2021 · if fB f B and fS f S are both defined on X X (and if X X is not necessarily a subset of reals) then their composition is not well-defined. but of course, I think it's clear what you …

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 …

Oct 29, 2019 · To say "Ec E c is perfectly measurable" is simply an intensified way of saying "Ec E c is measurable". Perhaps it means "Ec E c obviously is measurable, because E E is …

Suppose there is a family (can be infinite) of measurable spaces. What are the usual ways to define a sigma algebra on their Cartesian product? There is one way in the context of defining …