Bernoulli sequences and Borel measurability in $(0,1)$

Veselý, Petr. "Bernoulli sequences and Borel measurability in $(0,1)$." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 341-346. <http://eudml.org/doc/247499>.

@article{Veselý1993,
abstract = {The necessary and sufficient condition for a function $f : (0,1) \rightarrow [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 $H : \lbrace 0,1 \rbrace ^\mathbb \{N\} \rightarrow \lbrace 0,1 \rbrace ^\mathbb \{N\}$ such that $\mathcal \{L\} (H(\text\{\bf X\}^p)) = \mathcal \{L\} (\text\{\bf X\}^\{1/2\})$ 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 $P[X^p_i = 1] = p$.},
author = {Veselý, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Borel measurable function; Bernoulli sequence of random variables; Strong law of large numbers; strong law of large numbers; Bernoulli sequence of random variables},
language = {eng},
number = {2},
pages = {341-346},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Bernoulli sequences and Borel measurability in $(0,1)$},
url = {http://eudml.org/doc/247499},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Veselý, Petr
TI - Bernoulli sequences and Borel measurability in $(0,1)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 341
EP - 346
AB - The necessary and sufficient condition for a function $f : (0,1) \rightarrow [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 $H : \lbrace 0,1 \rbrace ^\mathbb {N} \rightarrow \lbrace 0,1 \rbrace ^\mathbb {N}$ such that $\mathcal {L} (H(\text{\bf X}^p)) = \mathcal {L} (\text{\bf X}^{1/2})$ 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 $P[X^p_i = 1] = p$.
LA - eng
KW - Borel measurable function; Bernoulli sequence of random variables; Strong law of large numbers; strong law of large numbers; Bernoulli sequence of random variables
UR - http://eudml.org/doc/247499
ER -