In his Nash equilibrium paper, Glicksberg states that the payoff functions are continuous. Such a function is defined on the product of mixed strategies, which are the Borel probability measures on a compactum, endowed with the product of the weak topologies. The continuity property is used in...

We show, by employing a density result for probability measures, that in games with a finite number of players and infinite-dimensional pure strategy spaces Nash equilibria can be approximated by finite mixed strategies. Given < epsilon >0, each player receives an expected utility payoff < epsilon >/2 close to his...</epsilon></epsilon>