# atom (measure theory)

Let $(X,\mathcal{B},\mu)$ be a measure space. A set $A\in\mathcal{B}$ is called an atom if $A$ has positive measure and contains no measurable subsets $B\subset A$ such that $0<\mu(B)<\mu(A)$.

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) AtommeasureTheory 2013-03-22 17:38:31 2013-03-22 17:38:31 asteroid (17536) asteroid (17536) 4 asteroid (17536) Definition msc 28A05 atom