Let be a tree defined on a metric over a set of paths such that the distance between paths and is , where is the number of nodes shared by and . Let 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 . Then one of the players has a winning Strategy in this Game.

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1999-05-26