Zero-full law for well approximable sets in missing digit sets

Bing Li, Ruofan Li, Yufeng Wu

Let $b\ge 3$ be an integer and $C(b,D)$ be the set of real numbers in $[0,1]$ whose base $b$ expansion only consists of digits in a set $D\subseteq \{0,...,b-1\}$. We study how…