Relations between Shy Sets and Sets of $ν_p$-Measure Zero in Solovay’s Model

G. Pantsulaia

Relations between Shy Sets and Sets of

ν_{p}

-Measure Zero in Solovay’s Model

G. Pantsulaia

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004), p. 63-69 / Harvested from The Polish Digital Mathematics Library

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Résumé

An example of a non-zero non-atomic translation-invariant Borel measure $ν_{p}$ on the Banach space $ℓ_{p} (1 \leq p \leq \infty)$ is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition " $ν_{p}$ -almost every element of $ℓ_{p}$ has a property P" implies that “almost every” element of $ℓ_{p}$ (in the sense of [4]) has the property P. It is also shown that the converse is not valid.

Publié le : 2004-01-01

Zbl 1109.28002

EUDML-ID : urn:eudml:doc:280853

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     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},
     volume = {52},
     year = {2004},
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G. Pantsulaia. Relations between Shy Sets and Sets of $ν_p$-Measure Zero in Solovay’s Model. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 63-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-7/