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arXiv · 1802.08574

Strong measure zero and meager-additive sets through the prism of fractal measures

Ondrej Zindulka
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Abstract

We develop a theory of \emph{sharp measure zero} sets that parallels Borel's \emph{strong measure zero}, and prove a theorem analogous to Galvin-Myscielski-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 $f:2^\omega\to2^\omega$ is continuous and $X$ is meager-additive, then so is $f(X)$.

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BibTeXRIS

Ondrej Zindulka. 2018-02-22. Strong measure zero and meager-additive sets through the prism of fractal measures. https://arxiv.org/abs/1802.08574

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