All Questions

This question asks for intuition, not a proof. An earlier question, Measures of non-abelian-ness was thoroughly answered by Arturo Magidin. A paper by Gustafson1 proves that, for a nonabelian group, ...

Let $G$ be a finite group. It has been shown that: If the probability that two randomly selected elements of $G$ generate an abelian group is greater than $5/8$, $G$ is abelian. If the probability ...

Suppose $G$ is a locally compact compactly generated group. Let $\mu$ be a probability measure that is: Adapted to $G$, i.e. there is no proper subgroup $H$ such that $\mu(H)=1$. Symmetric, i.e. $\...

Let $G$ be a compact topological group (feel free to add hypotheses if necessary). Is there any mean value theorem for its (normalized to 1) Haar integral? In general, are there mean value theorems ...