CompletionDefinition of completion In a measure space , all subsets satisfying belong to . Completion of measure space . Let's write (symmetric difference of and ). For , if satisfying , then the entire is defined as . is a additive class. Let's consider satisfying the above conditions with respect to and define . The measure space is complete, and it is also the smallest extension. Outer measure completion In measure space , let's define . is an outer measure. is equal to the completion of [0]Top |