Abstract
This article aims to introduce some concepts such as complete outer measure on a σ – field and extension of outer measure on a σ – field. We discuss some properties of these concepts. Furthermore, the notion of outer measure relative to the σ – field has been studied as stronger form of null-additive relative to the σ – field. Finally, aims to introduce a new space noted by complete outer measure space and we present a theorem of the unique smallest complete extension outer measure space.
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