Parthasarathy's Theorem

In mathematics and in particular the study of games on the unit square, Parthasarathy's theorem is a generalization of Von Neumann's minimax theorem. It states that a particular class of games has a mixed value, provided that at least one of the players has a strategy that is restricted to absolutely continuous distributions with respect to the Lebesgue measure (in other words, one of the players is forbidden to use a pure strategy).

The theorem is attributed to the Indian mathematician Thiruvenkatachari Parthasarathy.

terminology: and stand for the unit interval ; is the set of probability distributions on ( defined similarly); is the set of class of absolutely continuous distributions on ( defined similarly).