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Erschienen in:
2017 | OriginalPaper | Buchkapitel
4. Measure Theory
verfasst von : William P. Ziemer
Erschienen in: Modern Real Analysis
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Abstract
An outer measure on an abstract set X is a monotone, countably subadditive function defined on all subsets of X. In this section, the notion of measurable set is introduced, and it is shown that the class of measurable sets forms a \(\sigma \)-algebra, i.e., measurable sets are closed under the operations of complementation and countable unions. It is also shown that an outer measure is countably additive on disjoint measurable sets.