Real Analysis Exchange

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

Stewart Baldwin and Jack Brown

Full-text: Open access


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

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

First available in Project Euclid: 28 September 2010

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Complete Boolean Algebra Marczewski Measurable


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.

Export citation