A WEAK LAW OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES.

Each sequence f1, f2, ... of random variables satisfying limM→∞ (M supk∈N P(|fk| > M)) = 0 contains a subsequence fk1, fk2, ??? which, along with all its subsequences, satisfies the weak law of large numbers limN→∞ ((1/N) ∑n=1N fkn -- DN) = 0 in probability. Here, DN is a "corrector" random variable with values in [--N, N] for each N ∈ N; these correctors are all equal to zero if, in addition, lim infn→∞ E (fn² 1{|fn|≤M})) = 0 for every M ∈ (0, ∞). [ABSTRACT FROM AUTHOR]