Geodesic
Strong measure zero and meager-additive sets through the prism of fractal measures
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 1, pp. 131-155.

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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 $2^{\omega}$ is meager-additive if and only if it is $\mathcal E$-additive; if $f\colon 2^{\omega}\to 2^{\omega}$ is continuous and $X$ is meager-additive, then so is $f(X)$.
DOI : 10.14712/1213-7243.2015.277
Classification : 03E05, 03E20, 28A78
Keywords: meager-additive; $\mathcal E$-additive; strong measure zero; sharp measure zero; Hausdorff dimension; Hausdorff measure 
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Zindulka, Ondřej. Strong measure zero and meager-additive sets through the prism of fractal measures. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 1, pp. 131-155. doi : 10.14712/1213-7243.2015.277. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.277/

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