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, …

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.

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 …

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 …

What does it mean by $\mathcal {F}$-measurable? Ask Question Asked 12 years, 2 months ago Modified 8 years, 11 months ago

Thank you, Daniel for the elucidation. It is very much appreciated - spent 2 hours trying to make sense out of the proof and so I decided to come here. It's the first one I've encountered in this …

Nov 25, 2024 · Related questions: Why do we define measurable sets as a $\sigma$-algebra, not just an algebra? Why is $\sigma$-algebra necessary to define a measure?

Nov 1, 2012 · As a $ \sigma $-algebra is by definition closed under a countable union, and as singletons in $ \mathbb {R} $ are Borel-measurable, it follows that a countable subset of $ …

Oct 27, 2023 · A measurable function is then a function $f: X \to Y$ that preserves the measurable property of the spaces on which it is defined.

May 17, 2020 · Is it an implication of the definition? If yes, how is it avoiding admitting non-measurable sets into sigma algebra? When they say measurable/non-measurable, what is the …