CONVERGENCE OF ADAPTED SEQUENCES IN BANACH SPACES WITHOUT THE RANDON-NIKODYM PROPERTY

Dinh Quang Luu

Abstract

           An adapted sequence (X_n ) of Pettis integrable functions is said to be a game fairer with time iff for every ε > 0 there exists p ∈ N such that for all n ≥ q ≥ p we have P( ||E_q(X_n) - X_q|| > ε) < ε. We prove some Pettis mean and almost sure convergence results for such games in Banach spaces without the Radon-Nikodym property.