Mapping Borel sets onto balls and self-similar sets by Lipschitz and nearly Lipschitz maps

Ondřej Zindulka

If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu (N)>0$, an ultr…