## Real Analysis Exchange

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

#### 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