atom (measure theory)

Let $(X,ℬ,\mu )$ be a measure space. A set $A\in ℬ$ is called an atom if $A$ has positive measure and contains no measurable subsets $B\subset A$ such that .

An equivalent definition can be: $A$ has positive measure and for every measurable subset $B\subset A$, either $\mu (B)=0$ or $\mu (A-B)=0$.

Title	atom (measure theory)
Canonical name	AtommeasureTheory
Date of creation	2013-03-22 17:38:31
Last modified on	2013-03-22 17:38:31
Owner	asteroid (17536)
Last modified by	asteroid (17536)
Numerical id	4
Author	asteroid (17536)
Entry type	Definition
Classification	msc 28A05
Synonym	atom