All Questions

Hillel Furstenberg conjectured that the only $2$-$3$-invariant probability measure on the circle without atoms is the Lebesgue measure. More precisely: Question: (Furstenberg) Let $\mu$ be a ...

Let $(X,\Sigma)$ be a measurable space [which we can assume to be a standard Borel space if we wish]. Let $\mathcal{S}$ be a set of probability measures on $(X,\Sigma)$. [If we wish, we can assume ...