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A set $X\subseteq\mathbb{R}$ is strong measure zero if, for every sequence $(\epsilon_i)_{i\in\mathbb{N}}$ of positive reals, there is a sequence $(I_i)_{i\in\mathbb{N}}$ of open intervals covering $X$...

Beyond measure zero we have yet another measure-y notion of smallness: strong measure zero. A set $S\subseteq\mathbb{R}$ is strong measure zero if, for any $f:\mathbb{N}\rightarrow\mathbb{R}_{>0}$, ...

This question is essentially an expanded version of the unanswered half of Two strengthenings of "strong measure zero". A set $X$ of reals is strong measure zero if, for any $f: \omega\...