A generalization of Kuhn's theorem for an infinite game

An extensive ^-person game is usually described in terms of a finite tree in an oriented plane. The game involves in its structure the mixed and behavior strategies of each player closely related to some specified information sets. Under the assumption that each move possesses at least two alternatives, H.W. Kuhn [1] proved the theorem that the game has perfect recall if and only if, given any mixed strategies μu β2, •••, βn, there may be associated with them behavior strategies βu /32, •••, /?», each /?,depending only on the corresponding mixed strategy /*,-, so that they give rise to the equalities,