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.
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Ziemer, W.P. (2017). Measure Theory. In: Modern Real Analysis. Graduate Texts in Mathematics, vol 278. Springer, Cham. https://doi.org/10.1007/978-3-319-64629-9_4
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DOI: https://doi.org/10.1007/978-3-319-64629-9_4
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-64629-9
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