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

• Autorzy: G. Pantsulaia
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
• 03C50: Models with special properties (saturated, rigid, etc.)
• 28D05: Measure-preserving transformations
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 1
• Strony: 63-69

Daty

wydano

2004

Twórcy

autor

G. Pantsulaia

• Department of Mathematics, Georgian Technical University, Kostava Street 77, 01075 Tbilisi 75, Georgia

Identyfikatory

DOI

10.4064/ba52-1-7