Measures and Probabilities

  • Michel Simonnet

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Integration Relative to Daniell Measures

    1. Front Matter
      Pages 1-1
    2. Michel Simonnet
      Pages 3-25
    3. Michel Simonnet
      Pages 26-39
    4. Michel Simonnet
      Pages 40-85
    5. Michel Simonnet
      Pages 86-92
    6. Michel Simonnet
      Pages 93-120
    7. Michel Simonnet
      Pages 121-132
    8. Michel Simonnet
      Pages 133-165
    9. Michel Simonnet
      Pages 166-171
  3. Operations on Measures Defined on Semirings

    1. Front Matter
      Pages 173-173
    2. Michel Simonnet
      Pages 175-192
    3. Michel Simonnet
      Pages 193-223
    4. Michel Simonnet
      Pages 224-241
    5. Michel Simonnet
      Pages 242-264
    6. Michel Simonnet
      Pages 265-285
    7. Michel Simonnet
      Pages 286-308
  4. Convergence of Random Variables; Conditional Expectation

    1. Front Matter
      Pages 309-309
    2. Michel Simonnet
      Pages 311-325
    3. Michel Simonnet
      Pages 326-343

About this book

Introduction

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.

Keywords

Conditional probability Covariance matrix Ergodic theory Law of large numbers Median Random variable Variance convergence of random variables measure theory statistics

Authors and affiliations

  • Michel Simonnet
    • 1
  1. 1.Department of MathematicsUniversity of DakarSenegal

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4012-9
  • Copyright Information Springer-Verlag New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94644-3
  • Online ISBN 978-1-4612-4012-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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