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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Certain games, category, and measure


Author: Sławomir Solecki
Journal: Proc. Amer. Math. Soc. 119 (1993), 275-279
MSC: Primary 04A15; Secondary 04A20, 90D44
MathSciNet review: 1149979
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Abstract: For $ A \subset {2^\omega }$ and $ X \subset \omega $ consider an infinite game $ \Gamma (A,X)$ in which two players I and II choose $ {c_n} \in \{ 0,1\} $. $ {c_n}$ is chosen by I if $ n \in X$ and by II if $ n \in \omega \backslash X$. I wins if $ ({c_0},{c_1},{c_2}, \ldots ) \in A$. We analyze connections between $ A$ and the family of all sets $ X \subset \omega $ for which I has a winning strategy in $ \Gamma (A,X)$. Certain similarities and differences appear if one formulates these connections in the language of category and of Lebesgue measure.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1149979-X
Keywords: Infinite games, category, measure
Article copyright: © Copyright 1993 American Mathematical Society