Real Analysis Exchange

Some remarks on additive properties of invariant σ-ideals on the real line

A. B. Kharazishvili

Full-text: Open access

Abstract

We consider some additive properties of invariant \(\sigma\)-ideals and \(\sigma\)-algebras of subsets of the real line \({\mathbb{R}}\). In particular, we generalize two classical Sierpinski results, concerning additive properties of measure and category on \({\mathbb{R}}\), to a large class of invariant \(\sigma\)-ideals and \(\sigma\)-algebras.

Article information

Source
Real Anal. Exchange, Volume 21, Number 2 (1995), 715-724.

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1339694100

Mathematical Reviews number (MathSciNet)
MR1407284

Zentralblatt MATH identifier
0879.28026

Subjects
Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28D05: Measure-preserving transformations

Keywords
real line invariant \(\sigma\)--ideal \(\sigma\)-algebra countable chain condition Hamel base

Citation

Kharazishvili, A. B. Some remarks on additive properties of invariant σ-ideals on the real line. Real Anal. Exchange 21 (1995), no. 2, 715--724. https://projecteuclid.org/euclid.rae/1339694100


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