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, known as …

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

Feb 28, 2015 · What is your exact definition of Lebesgue measurability? Because with the usual definition, the composition of two Lebesgue measurable functions is in general not measurable.

We are simply showing that the intersection of two measurable sets is again measurable. You are confusing properties of a measure function with what it means to be for a set to be measurable.

Feb 23, 2017 · A measurable function (might need to be bounded or of bounded variation - not sure!) is approximately continuous i.e. continuous except on a set of measure 0. Measurability is quite a …

Mar 12, 2016 · Using this, one can easily show that a Baire measurable homomorphism from a Baire group to a separable group is continuous (Pettis' theorem). See Kechris, Classical Descriptive Set …

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 function in …

What's your definition of measurability and w.r.t. what $\sigma$-algebras? Because from the point of view of the theory of general measurable spaces, your problem is the definition of measurability. …