atom (measure theory)

Let (X,,μ) be a measure spaceMathworldPlanetmath. A set A is called an atom if A has positive measure and contains no measurable subsets BA such that 0<μ(B)<μ(A).

An equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath definition can be: A has positive measure and for every measurable subset BA, either μ(B)=0 or μ(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