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.

# Borel Determinacy Theorem

## See also

Game Theory, Tree## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Borel Determinacy Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/BorelDeterminacyTheorem.html