Definition of a measurable function? - Mathematics Stack Exchange
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.
What does "measurable" mean intuitively? - Mathematics Stack …
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, …
analysis - What is the definition of a measurable set?
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 …
measure theory - What does it mean by $\mathcal {F}
I always see this word $\\mathcal{F}$-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 …
real analysis - Show that $f (x+y)=f (x)+f (y)$ implies $f
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 …
How do I think of a measurable function? - Mathematics Stack …
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 …
Prove if $E_1$ and $E_2$ are measurable, so is $E_1 \cap E_2$
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.
Infinite product of measurable spaces - Mathematics Stack Exchange
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 …
$f$ a real, continuous function, is it measurable?
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 …
what is the definition of a $\\mu$-measurable function?
On p. 6 of that textbook, it defines a $\mu$-measurable function as one which is measurable on the unique sigma algebra associated with the completion of the measure $\mu$.