Integration and Modern Analysis

Released on by John J. Benedetto
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  • Integration and Modern Analysis Book Detail

  • Author : John J. Benedetto
  • Release Date : 2010-01-08
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 589
  • ISBN 13 : 0817646566
  • File Size : 9,9 MB
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Integration and Modern Analysis by John J. Benedetto PDF Summary

Book Description: This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.

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