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 s0 and Y is a Sierpinski set, then X + Y has property s0 (Theorem 12). 3. If X is a meager set with property s0 and Y is a Lusin set, then X + Y has property s0 (Theorem 17). An infinite game is introduced, motivated by additive properties of certain classes of sets of real numbers. 1991 Mathematics Subject Classification. 90D44, 04A99.
| Original language | English |
|---|---|
| Pages (from-to) | 177-191 |
| Number of pages | 15 |
| Journal | Quaestiones Mathematicae |
| Volume | 16 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 1993 |
Keywords
- Game
- Hurewicz’s property
- Lusin set
- S0-set
- Sierpinski set
- Strong measure zero set
- Strong γ set
- Winning strategy
- γ set