| Title:
|
The $0-1$ law generalized for non-denumerable families of events and of $\sigma$-algebras of events (English) |
| Author:
|
Ho, Nguyen Van |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
4 |
| Year:
|
1976 |
| Pages:
|
296-300 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\sigma_t$, $t\in T$. () |
| MSC:
|
60F20 |
| idZBL:
|
Zbl 0349.60022 |
| idMR:
|
MR0426117 |
| DOI:
|
10.21136/AM.1976.103649 |
| . |
| Date available:
|
2008-05-20T18:05:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103649 |
| . |
| Reference:
|
[1] J. Neveu: Bases mathématiques du calcul des probabilités.Paris, 1964. Zbl 0137.11203, MR 0198504 |
| Reference:
|
[2] W. Feller: An introduction to probability theory and its applications.New York, 1966. Zbl 0138.10207, MR 0242202 |
| Reference:
|
[3] A. Rényi: Probability theory.Budapest, 1970. |
| Reference:
|
[4] И. И. Гихман А. В. Скороход: Теория случайных процессов.Москва, 1971. Zbl 1230.35094 |
| . |
