Definition:Complete Measure Space

Definition
Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let the family of $\mu$-null sets $\NN_\mu$ satisfy the condition:


 * $\forall N \in \NN_\mu: \forall M \subseteq N: M \in \NN_\mu$

That is, any subset of a $\mu$-null set is again a $\mu$-null set.

Then $\struct {X, \Sigma, \mu}$ is said to be a complete measure space.

Also see

 * Completion Theorem (Measure Space), showing that any measure space may be embedded in a complete measure space