Abstract
Abstract If X has strong measure zero aid if Y is contained in an F σ, set of measure zero, then X + Y has measure zero (Proposition 9). If X is a measure zero set with property s 0 and Y is a Sierpinski set, then X + Y has property s 0 (Theorem 12). If X is a meager set with property s 0 and Y is a Lusin set, then X + Y has property s 0 (Theorem 17). An infinite game is introduced, motivated by additive properties of certain classes of sets of real numbers.
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