ADDITIVE PROPERTIES OF SETS OF REAL NUMBERS AND AN INFINITE GAME

Abstract

1. 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).

2. 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).

3. 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.