Definition:Complete Measure Space

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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

  • Results about complete measure spaces can be found here.


Sources