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Standard measure spaces

In: Measure and Integration

Author

Listed:
  • Hari Bercovici

    (Indiana University, Department of Mathematics)

  • Arlen Brown

    (Indiana University, Department of Mathematics)

  • Carl Pearcy

    (Texas A&M University, Department of Mathematics)

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).

Suggested Citation

  • Hari Bercovici & Arlen Brown & Carl Pearcy, 2016. "Standard measure spaces," Springer Books, in: Measure and Integration, edition 1, chapter 0, pages 265-284, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-29046-1_11
    DOI: 10.1007/978-3-319-29046-1_11
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