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On the strong law of large numbers for blockwise independent and blockwise orthogonal random variables. (English. Russian original) Zbl 0847.60022

Theory Probab. Appl. 39, No. 4, 677-684 (1994); translation from Teor. Veroyatn. Primen. 39, No. 4, 804-812 (1994).
Some analogues of the Kolmogorov and Menshov-Rademacher SLLN’s are established for a sequence \(\{X_n\}^\infty_{n = 1}\) of blockwise independent or orthogonal r.v.’s. The latter means that for any \(k \in \mathbb{N}\) and a block \(\Delta_k = [w(k), w(k + 1))\) where \(1 = w(1) < w(2) < \dots\) the system \(\{X_m\}_{m \in \Delta_k}\) consists of independent (or orthogonal) r.v.’s. It is shown that the proposed sufficient conditions are in a sense the best possible.

MSC:

60F15 Strong limit theorems
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