Borel determinacy is the assertion that every infinite two-player game of perfect information played along a tree is determined when the paths won by the first player form a Borel set. A game is determined if one of its players has a winning strategy. The Borel determinacy theorem establishes this assertion (Martin 1975).
Borel Determinacy
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References
Martin, D. A. "Borel Determinacy." Ann. Math. 102, 363-371, 1975. https://doi.org/10.2307/1971035.Cite this as:
Weisstein, Eric W. "Borel Determinacy." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BorelDeterminacy.html