| A Classification of
a Martingale - Like Sequences Dinh Quang Luu Abstract A \se Xn is said to be a game fairer with time if for every $\ve>0$ we have $\scriptstyle{\lim\limits_n \sup\limits_{m > n}P \bigl(||E_n(X_m)-X_n||>\ve\bigr)=0}$. It is known that every L1-bounded Banach space-valued game fairer with time has a unique Riesz-Talagrand decomposition: Xn = Mn + Pn, where (Mn) is a uniformly integrable \ma and (Pn) \ctz in probability. The aim of this te is to give a classification of a class of martingale-like sequences considerably more general than games fairer with time for which the above Riesz-Talagrand \de still holds. |