Relations between Shy Sets and Sets of
$\nu _p$-Measure Zero in Solovay's Model
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 63-69
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
An example of a non-zero non-atomic translation-invariant Borel measure $\nu _p$ on the Banach space $\ell _p (1\le p \le \infty )$ is constructed in Solovay's model. It is established that, for $1 \le p \infty ,$ the condition “$\nu _p$-almost every element of ${\ell }_p$ has a property $P$” implies that “almost every” element of $\ell _p$ (in the sense of [4]) has the property $P$. It is also shown that the converse is not valid.
Keywords:
example non zero non atomic translation invariant borel measure banach space ell infty constructed solovays model established infty condition p almost every element ell has property implies almost every element ell sense has property shown converse valid
Affiliations des auteurs :
G. Pantsulaia 1
@article{10_4064_ba52_1_7,
author = {G. Pantsulaia},
title = {Relations between {Shy} {Sets} and {Sets} of
$\nu _p${-Measure} {Zero} in {Solovay's} {Model}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {63--69},
year = {2004},
volume = {52},
number = {1},
doi = {10.4064/ba52-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba52-1-7/}
}
TY - JOUR AU - G. Pantsulaia TI - Relations between Shy Sets and Sets of $\nu _p$-Measure Zero in Solovay's Model JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2004 SP - 63 EP - 69 VL - 52 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/ba52-1-7/ DO - 10.4064/ba52-1-7 LA - en ID - 10_4064_ba52_1_7 ER -
%0 Journal Article %A G. Pantsulaia %T Relations between Shy Sets and Sets of $\nu _p$-Measure Zero in Solovay's Model %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2004 %P 63-69 %V 52 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/ba52-1-7/ %R 10.4064/ba52-1-7 %G en %F 10_4064_ba52_1_7
G. Pantsulaia. Relations between Shy Sets and Sets of $\nu _p$-Measure Zero in Solovay's Model. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 63-69. doi: 10.4064/ba52-1-7
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