| Title:
|
Bernoulli sequences and Borel measurability in $(0,1)$ (English) |
| Author:
|
Veselý, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
341-346 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The necessary and sufficient condition for a function $f : (0,1) \to [0,1] $ to be Borel measurable (given by Theorem stated below) provides a technique to prove (in Corollary 2) the existence of a Borel measurable map $H : \{ 0,1 \}^\Bbb N \to \{ 0,1 \}^\Bbb N$ such that $\Cal L (H(\text{\bf X}^p)) = \Cal L (\text{\bf X}^{1/2})$ holds for each $p \in (0,1)$, where $\text{\bf X}^p = (X^p_1 , X^p_2 , \ldots )$ denotes Bernoulli sequence of random variables with $P[X^p_i = 1] = p$. (English) |
| Keyword:
|
Borel measurable function |
| Keyword:
|
Bernoulli sequence of random variables |
| Keyword:
|
Strong law of large numbers |
| MSC:
|
28A20 |
| MSC:
|
60A10 |
| idZBL:
|
Zbl 0777.60003 |
| idMR:
|
MR1241742 |
| . |
| Date available:
|
2009-01-08T18:03:49Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118586 |
| . |
| Reference:
|
[1] Feller W.: An Introduction to Probability Theory and its Applications. Volume II..John Wiley & Sons, Inc. New York, London and Sydney (1966). MR 0210154 |
| Reference:
|
[2] Štěpán J.: Personal communication.(1992). |
| . |
