Standard measure spaces

Hari Bercovici, Arlen Brown and Carl Pearcy
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Hari Bercovici: Indiana University, Department of Mathematics
Arlen Brown: Indiana University, Department of Mathematics
Carl Pearcy: Texas A&M University, Department of Mathematics

Chapter Chapter 11 in Measure and Integration, 2016, pp 265-284 from Springer

Abstract: 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).

Keywords: Standard Measure Space; Isomorphism; Natural Notion; Countable Union; Measurable Bijection (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-29046-1_11

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