Borel Determinacy Theorem

Let T be a tree defined on a metric over a set of paths such that the distance between paths p and q is 1/n, where n is the number of nodes shared by p and q. Let A be a Borel set of paths in the topology induced by this metric. Suppose two players play a game by choosing a path down the tree, so that they alternate and each time choose an immediate successor of the previously chosen point. The first player wins if the chosen path is in A. Then one of the players has a winning strategy in this game.

See also

Game Theory, Tree

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Cite this as:

Weisstein, Eric W. "Borel Determinacy Theorem." From MathWorld--A Wolfram Web Resource.

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