# Measure Algebras

## TL;DR

This paper characterizes measure algebras as Boolean σ-algebras that are both weakly distributive and uniformly concentrated, providing a precise algebraic condition for measure algebra identification.

## Contribution

It offers a new algebraic characterization of measure algebras based on weak distributivity and uniform concentration properties.

## Key findings

- Measure algebras are exactly Boolean σ-algebras that are weakly distributive and uniformly concentrated.
- Provides a necessary and sufficient condition for a Boolean σ-algebra to be a measure algebra.
- Connects algebraic properties with measure-theoretic concepts in Boolean algebras.

## Abstract

A Boolean $\sigma$-algebra $B$ is a measure algebra if and only if it is weakly distributive and uniformly concentrated.