Real Analysis Exchange

On Marczewski-Burstin Like Characterizations of Certain σ-Algebras and σ-Ideals

Hussain Elalaoui-Talibi

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Consider a $\sigma$-ideal, $\sigma$-algebra pair $\cal{I} \subseteq \cal{A}$ on a Polish space $X$ which has no isolated points, such that $\cal{A}$ contains all the Borel subsets of $X$ while $\cal{I}$ contains all the countable subsets of $X$, but none of the perfect subsets of $X$. We show that if $(\cal{I}, \cal{A})$ admits a simultaneous MB-like characterization consisting of Borel sets, then $(\cal{I},\cal{A})$ is $((s_{0}), (s))$, the $\sigma$-ideal, $\sigma$-algebra pair of Marczewski null, Marczewski measurable sets. We deduce some results about uniformly completely Ramsey sets.

Article information

Real Anal. Exchange, Volume 26, Number 1 (2000), 413-416.

First available in Project Euclid: 2 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 26E99: None of the above, but in this section 04A05

MB-like characterization Marczewski-measurable completely Ramsey


Elalaoui-Talibi, Hussain. On Marczewski-Burstin Like Characterizations of Certain σ-Algebras and σ-Ideals. Real Anal. Exchange 26 (2000), no. 1, 413--416.

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