A note concerning the L1convergence of a class of games which become fairer with time

Abstract

Throughout this note, let be a probability space with an increasing sequence of sub σ-fields of whose union generates . Let be a sequence of random variables adapted to (see [3], p. 65) and henceforth be referred to as a game. As in [1], the game will be said to become fairer with time if, for every ε > ε,as n, m → ∞ with n ≧ m