All Questions

The Banach-Tarski paradox states that for a solid ball in 3‑dimensional space, there exists a decomposition into a finite number of disjoint subsets, which can then be put back together in a different ...

Let $\mathbb{R}$ act on itself by translation. Then there is no finite decomposition of a unit interval into pieces which, when translated, yields two distinct unit intervals. More formally does ...

More precisely, I would like to know which implications between the following definitions of amenability of a discrete countable (or even finitely generated) group can be proved to hold with only ZF (...

The question is in the title, amenability being understood as the existence of a left-invariant finitely additive probability measure on the group of interest. The case of countable groups is treated ...