The strong law of large numbers for m-orthogonal random variables. (English. Russian original) Zbl 0628.60041

Radchenko, V. N.

Theory Probab. Math. Stat. 33, 111-115 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 100-103 (1985).

Consider a random array \(\{\) X(k): \(k=(k_ 1,,k_ r)\in N^ r\}\) with properties E \(X^ 2(k)<\infty\) and E X(k) X(\(\ell)=0\) if \(\max (| k_ 1-\ell_ 1|,...,| k_ r-\ell_ r|)>m\). The author proves a generalization of the Menshov-Rademacher theorem and gives a sufficient condition for the strong law of large numbers. The proofs are based on a maximal inequality due to the reviewer [Acta Sci. Math. 39, 353-366 (1977; Zbl 0363.60022)].

Reviewer: F.Móricz

MSC:

60F15	Strong limit theorems
60G60	Random fields
60E15	Inequalities; stochastic orderings

Keywords:

Menshov-Rademacher theorem; strong law of large numbers; maximal inequality

Citations:

Zbl 0363.60022