Abstract
There are many examples of measure spaces that present various pathologies and on which some of the deeper theorems of measure theory fail. Elements of the class of standard measure spaces, to be defined shortly, do not display any of these pathologies and, in addition, can be classified up to a natural notion of isomorphism. The results we present here use little in addition to the observation that a separable metric space can be written as a countable union of closed subsets of arbitrarily small diameter (for instance, the closed balls of a fixed radius centered at the points of a countable dense set).
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© 2016 Springer International Publishing Switzerland
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Bercovici, H., Brown, A., Pearcy, C. (2016). Standard measure spaces. In: Measure and Integration. Springer, Cham. https://doi.org/10.1007/978-3-319-29046-1_11
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DOI: https://doi.org/10.1007/978-3-319-29046-1_11
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29044-7
Online ISBN: 978-3-319-29046-1
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