Sequences of m-orthogonal random variables

A sequence of random variables {X_n} is said to be a sequence of m -orthogonal random variables if E X _n ² < for any n and E(X_kX_j) for k–j>m. Here m is a nonnegative integer. One proves a theorem on the law of the iterated logarithm for a sequence ofm-orthogonal random variables.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 119, pp. 198–202, 1982.