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, TreeExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Borel Determinacy Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BorelDeterminacyTheorem.html