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, known as …

Nov 29, 2024 · Measurable of a vector-valued function Ask Question Asked 1 year, 2 months ago Modified 1 year, 2 months ago

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 …

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.

Closure, Interior, and Boundary of Jordan Measurable Sets. Ask Question Asked 13 years, 3 months ago Modified 10 years, 2 months ago

Mar 21, 2024 · Let (X, σ) (X, σ) and (Y, ν) (Y, ν) are measurable space and f: X Y f: X Y is a map that takes each measurable set of σ σ to a measurable set of ν ν, then is f f needed to be measurable, i.e …

Feb 3, 2018 · Explore related questions measure-theory measurable-functions See similar questions with these tags.

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 $ \mathbb {R} $ is …

Nov 1, 2024 · I am trying to understand why Lp L p -spaces of functions on a measure space X X are defined as composed of classes of measurable functions, while it is obviously possible to generalise …

Mar 14, 2022 · Stochastic Processes: Measurable vs Progressively Measurable Ask Question Asked 3 years, 10 months ago Modified 3 years, 10 months ago