Geodesic
Relations between Shy Sets and Sets of $\nu _p$-Measure Zero in Solovay's Model
G. Pantsulaia1
1 Department of Mathematics Georgian Technical University Kostava Street 77 01075 Tbilisi 75, Georgia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 63-69.

Voir la notice de l'article provenant de 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.
DOI : 10.4064/ba52-1-7
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

G. Pantsulaia 1

1 Department of Mathematics Georgian Technical University Kostava Street 77 01075 Tbilisi 75, Georgia 
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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. http://geodesic.mathdoc.fr/articles/10.4064/ba52-1-7/

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