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  3. Absolute Measurable Spaces
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2010
      May 2008
      ISBN:
      9780511721380
      9780521875561
      DOI:
      https://doi.org/10.1017/CBO9780511721380
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.62kg, 292 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Abstract Analysis
      Series:
      Encyclopedia of Mathematics and its Applications (120)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Abstract Analysis
    Series:
    Encyclopedia of Mathematics and its Applications (120)
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    Book description

    Absolute measurable space and absolute null space are very old topological notions, developed from well-known facts of descriptive set theory, topology, Borel measure theory and analysis. This monograph systematically develops and returns to the topological and geometrical origins of these notions. Motivating the development of the exposition are the action of the group of homeomorphisms of a space on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures on the unit cube, and the extensions of this theorem to many other topological spaces. Existence of uncountable absolute null space, extension of the Purves theorem and recent advances on homeomorphic Borel probability measures on the Cantor space, are among the many topics discussed. A brief discussion of set-theoretic results on absolute null space is given, and a four-part appendix aids the reader with topological dimension theory, Hausdorff measure and Hausdorff dimension, and geometric measure theory.

    Reviews

    'The monograph nicely connects classical ideas and examples with newer investigations. … should be very useful for a wide audience of graduate students and researchers.'

    Source: Mathematical Reviews

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