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The $0-1$ law generalized for non-denumerable families of events and of $\sigma$-algebras of events
Applications of Mathematics, Tome 21 (1976) no. 4, pp. 296-300 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\sigma_t$, $t\in T$.
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 $\sigma_t$, $t\in T$.
DOI : 10.21136/AM.1976.103649
Classification : 60F20 
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Ho, Nguyen Van. The $0-1$ law generalized for non-denumerable families of events and of $\sigma$-algebras of events. Applications of Mathematics, Tome 21 (1976) no. 4, pp. 296-300. doi: 10.21136/AM.1976.103649

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