A note on the distribution of the digits in Cantor expansions

On exceptional sets in Erdős–Rényi limit theorem revisited

“…Moreover, in a complete metric space a set is residual if it contains a dense G δ set, see [23]. Recent results show that certain exceptional sets can also be large from the topological point of view, see, for example, [4,5,5,12,15,16,17,18,21] and references therein. In [19] the authors also showed that is either residual or empty.…”