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The notions lim sup $A_n$, lim inf $A_n$ for sequences of sets $A_n$ and the notion lim sup $\sigma_n$ for sequences of $\sigma$-algebras $\sigma_n$ are generalized for nondenumerable families of sets, or $\sigma$-algebras, respectively. Using these generalized definitions, the author proves a certain weaker analogue of the Borel-Cantelli lemma for non-denumerable families of sets $A_n$, $t\in T$, and a direct generalization of the Kolmogorov $0-1$ law for non-denumerable families of $\sigma$-algebras $\sigma_t$, $t\in T$.
[1] J. Neveu: Bases mathématiques du calcul des probabilités. Paris, 1964. MR 0198504 | Zbl 0137.11203
[2] W. Feller: An introduction to probability theory and its applications. New York, 1966. MR 0242202 | Zbl 0138.10207
[3] A. Rényi: Probability theory. Budapest, 1970.
[4] И. И. Гихман А. В. Скороход: Теория случайных процессов. Москва, 1971. Zbl 1230.35094
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