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 $fcolon 2^{omega}o 2^{omega}$ is continuous and $X$ is meager-additive, then so is $f(X)$.
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机译：我们开发了一种与Borel的强度量零相似的尖锐度量零集理论，并证明了一个类似于Galvin-Mycielski-Solovay定理的定理，即，当且仅当它是微加性时，一组实数才具有尖锐度量零。一些后果$ 2 ^ { omega} $的子集只有且仅当$ mathcal E $可加时才是微加。如果$ f 冒号2 ^ { omega} 至2 ^ { omega} $是连续的，而$ X $是微加的，那么$ f（X）$也是。
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