Real Analysis Exchange

A Simple Proof That (s)/(s0) is a Complete Boolean Algebra

Stewart Baldwin and Jack Brown

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Abstract

Let $X$ be a complete separable metric space, let $(s)$ be the set of all Marczewski \cite{sm} measurable subsets of $X$, and let $(s^0)$ be the the set of all Marczewski null subsets of $X$. It is already known that $(s)/(s^0)$ is a complete Boolean algebra, but the known proofs of this involve complicated preliminaries. We present a simple proof that $(s)/(s^0)$ is a complete Boolean algebra.

Article information

Source
Real Anal. Exchange, Volume 24, Number 2 (1999), 855-859.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.rae/1285689160

Mathematical Reviews number (MathSciNet)
MR1704759

Zentralblatt MATH identifier
0967.28002

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

Keywords
Complete Boolean Algebra Marczewski Measurable

Citation

Baldwin, Stewart; Brown, Jack. A Simple Proof That ( s )/( s 0 ) is a Complete Boolean Algebra. Real Anal. Exchange 24 (1999), no. 2, 855--859. https://projecteuclid.org/euclid.rae/1285689160


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