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.
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Editorial Reviews
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"The monograph nicely connects classical ideas and examples with newer investigations. The book should be very useful for a wide audience of graduate students and researchers. Starting from basic considerations the reader is gently led to more advanced results and methods. Thanks to an in-depth treatment of the subject, several concepts are thoroughly developed."
Marek Balcerzak, Mathematical Reviews
Marek Balcerzak, Mathematical Reviews
Book Description
This monograph systematically develops and returns to the topological and geometrical origins of absolute measurable space. The existence of uncountable absolute null space and extension of the Purves theorem are among the many topics discussed. The exposition will suit researchers and graduate students of real analysis, set theory and measure theory.
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absolute measurable space, universally null set, strong measure zero sets, perfect set model, universally measurable map, other singular sets, separable metrizable space, universally measurable set, triangulable space, topological copy, homeomorphism group, topological copies, completely metrizable space, universally measurable function, uncountable order, whence card, ternary set, first category set, metrizable spaces, rectangular subdivision, collection univ, opaque sets, measurable spaces, uncountable subset, whenever card Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Q-finite Borel, Prove Theorem, Lebesgue-like Borel, Bruckner Davies-Goffman, Radon Nikodym, Prove Lemma, Continuum Hypothesis, Null Space Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
absolute measurable space, universally null set, strong measure zero sets, perfect set model, universally measurable map, other singular sets, separable metrizable space, universally measurable set, triangulable space, topological copy, homeomorphism group, topological copies, completely metrizable space, universally measurable function, uncountable order, whence card, ternary set, first category set, metrizable spaces, rectangular subdivision, collection univ, opaque sets, measurable spaces, uncountable subset, whenever card Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Q-finite Borel, Prove Theorem, Lebesgue-like Borel, Bruckner Davies-Goffman, Radon Nikodym, Prove Lemma, Continuum Hypothesis, Null Space Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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