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Measures and Probabilities

  • Textbook
  • © 1996

Overview

Authors:
  1. Michel Simonnet

    1. Department of Mathematics, University of Dakar, Senegal

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Part of the book series: Universitext (UTX)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Integration Relative to Daniell Measures

    1. Front Matter

      Pages 1-1
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    2. Riesz Spaces

      • Michel Simonnet
      Pages 3-25

    3. Measures on Semirings

      • Michel Simonnet
      Pages 26-39

    4. Integrable and Measurable Functions

      • Michel Simonnet
      Pages 40-85

    5. Lebesgue Measure on R

      • Michel Simonnet
      Pages 86-92

    6. Lp Spaces

      • Michel Simonnet
      Pages 93-120

    7. Integrable Functions for Measures on Semirings

      • Michel Simonnet
      Pages 121-132

    8. Radon Measures

      • Michel Simonnet
      Pages 133-165

    9. Regularity

      • Michel Simonnet
      Pages 166-171

  3. Operations on Measures Defined on Semirings

    1. Front Matter

      Pages 173-173
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    2. Induced Measures and Product Measures

      • Michel Simonnet
      Pages 175-192

    3. Radon-Nikodym Derivatives

      • Michel Simonnet
      Pages 193-223

    4. Images of Measures

      • Michel Simonnet
      Pages 224-241

    5. Change of Variables

      • Michel Simonnet
      Pages 242-264

    6. Stieltjes Integral

      • Michel Simonnet
      Pages 265-285

    7. The Fourier Transform in Rk

      • Michel Simonnet
      Pages 286-308

  4. Convergence of Random Variables; Conditional Expectation

    1. Front Matter

      Pages 309-309
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    2. The Strong Law of Large Numbers

      • Michel Simonnet
      Pages 311-325

    3. The Central Limit Theorem

      • Michel Simonnet
      Pages 326-343
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Keywords

About this book

Integration theory holds a prime position, whether in pure mathematics or in various fields of applied mathematics. It plays a central role in analysis; it is the basis of probability theory and provides an indispensable tool in mathe­ matical physics, in particular in quantum mechanics and statistical mechanics. Therefore, many textbooks devoted to integration theory are already avail­ able. The present book by Michel Simonnet differs from the previous texts in many respects, and, for that reason, it is to be particularly recommended. When dealing with integration theory, some authors choose, as a starting point, the notion of a measure on a family of subsets of a set; this approach is especially well suited to applications in probability theory. Other authors prefer to start with the notion of Radon measure (a continuous linear func­ tional on the space of continuous functions with compact support on a locally compact space) because it plays an important role in analysis and prepares for the study of distribution theory. Starting off with the notion of Daniell measure, Mr. Simonnet provides a unified treatment of these two approaches.

Authors and Affiliations

  • Department of Mathematics, University of Dakar, Senegal

    Michel Simonnet

Bibliographic Information

  • Book Title: Measures and Probabilities

  • Authors: Michel Simonnet

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-4012-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1996

  • Softcover ISBN: 978-0-387-94644-3Published: 06 June 1996

  • eBook ISBN: 978-1-4612-4012-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: 510

  • Topics: Probability Theory and Stochastic Processes

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