# Separable sigma algebra

(Redirected from Separable measure space)
In mathematics, σ-algebras are usually studied in the context of measure theory. A separable σ-algebra (or separable σ-field) is a σ-algebra $\mathcal{F}$ which is a separable space when considered as a metric space with metric $\rho(A,B) = \mu(A \triangle B)$ for $A,B \in \mathcal{F}$ and some measure $\mu$ (and with $\triangle$ being the symmetric difference operator).[citation needed] Note that any σ-algebra generated by a countable collection of sets is countable, but the converse need not hold.[citation needed]