## 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