Relations between Shy Sets and Sets of ${\nu }_p$-Measure Zero in Solovay’s Model

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 52.1 (2004): 63-69. <http://eudml.org/doc/280853>.

@article{G2004,
abstract = {An example of a non-zero non-atomic translation-invariant Borel measure $ν_p$ on the Banach space $ℓ_p (1 ≤ p ≤ ∞)$ 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.},
author = {G. Pantsulaia},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {translation-invariant Borel measure; prevalent set},
language = {eng},
number = {1},
pages = {63-69},
title = {Relations between Shy Sets and Sets of $ν_p$-Measure Zero in Solovay’s Model},
url = {http://eudml.org/doc/280853},
volume = {52},
year = {2004},
}

TY - JOUR
AU - G. Pantsulaia
TI - Relations between Shy Sets and Sets of $ν_p$-Measure Zero in Solovay’s Model
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 1
SP - 63
EP - 69
AB - An example of a non-zero non-atomic translation-invariant Borel measure $ν_p$ on the Banach space $ℓ_p (1 ≤ p ≤ ∞)$ 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.
LA - eng
KW - translation-invariant Borel measure; prevalent set
UR - http://eudml.org/doc/280853
ER -