Description

Book Synopsis

Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.

Published nearly forty years after the first edition, this long-awaited Second Edition also:

  • Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2
  • Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case
  • Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation

    • Table of Contents

    Preliminaries. Functions of Bounded Variation and the Riemann–Stieltjes Integral. Lebesgue Measure and Outer Measure. Lebesgue Measurable Functions. The Lebesgue Integral. Repeated Integration. Differentiation. Lp Classes. Approximations of the Identity and Maximal Functions. Abstract Integration. Outer Measure and Measure. A Few Facts from Harmonic Analysis. The Fourier Transform. Fractional Integration. Weak Derivatives and Poincaré–Sobolev Estimates.

Measure and Integral

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    £999.99

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    A Hardback by Richard L. Wheeden

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      View other formats and editions of Measure and Integral by Richard L. Wheeden

      Publisher: CRC Press
      Publication Date: 4/24/2015 12:00:00 AM
      ISBN13: 9781498702898, 978-1498702898
      ISBN10: 1498702899

      Description

      Book Synopsis

      Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.

      Published nearly forty years after the first edition, this long-awaited Second Edition also:

      • Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2
      • Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case
      • Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of HÃlder continuous functions and the space of functions of bounded mean oscillation

        • Table of Contents

        Preliminaries. Functions of Bounded Variation and the Riemann–Stieltjes Integral. Lebesgue Measure and Outer Measure. Lebesgue Measurable Functions. The Lebesgue Integral. Repeated Integration. Differentiation. Lp Classes. Approximations of the Identity and Maximal Functions. Abstract Integration. Outer Measure and Measure. A Few Facts from Harmonic Analysis. The Fourier Transform. Fractional Integration. Weak Derivatives and Poincaré–Sobolev Estimates.

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