Another martingale convergence theorem
Anthony G. Mucci · Pacific Journal of Mathematics · 1976
A classical martingale theorem is generalized to martingale like" sequences.The method of proof is a generalization of Doob's proof by "downcrossings".Introduction.Let (Ω, J3, P) be a probability space, {B n } an increasing sequence of sub sigma fields of B. Let {/ n , B n , n ^ 1} be an adapted sequence of P-integrable random variables.The sequence is said to be a martingale in the limit if lim sup \f n -E(f Λ \B n )\ = 0 P a.e.