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
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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 $\sigma_t$, $t\in T$.
@article{10_21136_AM_1976_103649,
author = {Ho, Nguyen Van},
title = {The $0-1$ law generalized for non-denumerable families of events and of $\sigma$-algebras of events},
journal = {Applications of Mathematics},
pages = {296--300},
publisher = {mathdoc},
volume = {21},
number = {4},
year = {1976},
doi = {10.21136/AM.1976.103649},
mrnumber = {0426117},
zbl = {0349.60022},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1976.103649/}
}
TY - JOUR AU - Ho, Nguyen Van TI - The $0-1$ law generalized for non-denumerable families of events and of $\sigma$-algebras of events JO - Applications of Mathematics PY - 1976 SP - 296 EP - 300 VL - 21 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1976.103649/ DO - 10.21136/AM.1976.103649 LA - en ID - 10_21136_AM_1976_103649 ER -
%0 Journal Article %A Ho, Nguyen Van %T The $0-1$ law generalized for non-denumerable families of events and of $\sigma$-algebras of events %J Applications of Mathematics %D 1976 %P 296-300 %V 21 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1976.103649/ %R 10.21136/AM.1976.103649 %G en %F 10_21136_AM_1976_103649
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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