Are their simple/natural examples of real-valued Borel-measurable random variables whose image is not a Borel set? Something that occurs "naturally"? I am teaching Doob's lemma (f …

A few questions, hopefully to spark some discussion. How can one define a product of measures? We could use Colombeau products by embedding the measures into the distributions? …

Let $(X,\|\cdot\|)$ be a Banach space and let $B(x; r)$ be the closed ball with radius $r$ around $x\in X$. Let $H(X)$ be the collection of all closed and bounded subsets of $X$. …

For some time, I have been stuck to the problem to be described as follows. The (perhaps not so commonly known) facts given here are taken from R. E. Edwards' Functional Analysis ( …