I am trying to solve exercise 1.9 in these notes, where we are asked to prove that $\mathcal{R} := \{ (x,g \cdot x) : x \in X, g \in G\}$ is a countable, probability measure preserving (p.m.p) equivalence relation whenever $G$ is a countable group acting on the standard probability space $(X, \mu...

I'm seeking a function that is non-Riemann integrable yet Lesbegue integrable. Everyone seems to illustrate this phenomenon with the indicator function applied to rational numbers. Is there another such function... perhaps one that would be of greater interest and background to students... one t...

I'm seeking a function that is non-Riemann integrable yet Lesbegue integrable. Everyone seems to illustrate this phenomenon with the indicator function applied to rational numbers. Is there another such function... perhaps one that would be of greater interest and background to students... one t...