Strong measure zero and meager-additive sets through the prism of fractal measures
Ondřej Zindulka (2019)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We develop a theory of sharp measure zero sets that parallels Borel’s strong measure zero, and prove a theorem analogous to Galvin–Mycielski–Solovay theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of is meager-additive if and only if it is -additive; if is continuous and is meager-additive, then so is .