Strong measure zero and infinite games
2017
We show that strong measure zero sets (in a \(\sigma \)-totally bounded metric space) can be characterized by the nonexistence of a winning strategy in a certain infinite game. We use this characterization to give a proof of the well known fact, originally conjectured by K. Prikry, that every dense \(G_\delta \) subset of the real line contains a translate of every strong measure zero set. We also derive a related result which answers a question of J. Fickett.
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