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Measure, Integral and Probability

  • Marek Capiński
  • Peter Ekkehard Kopp

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Marek Capiński, Peter Ekkehard Kopp
    Pages 1-13
  3. Marek Capiński, Peter Ekkehard Kopp
    Pages 15-51
  4. Marek Capiński, Peter Ekkehard Kopp
    Pages 53-69
  5. Marek Capiński, Peter Ekkehard Kopp
    Pages 71-114
  6. Marek Capiński, Peter Ekkehard Kopp
    Pages 115-143
  7. Marek Capiński, Peter Ekkehard Kopp
    Pages 145-169
  8. Marek Capiński, Peter Ekkehard Kopp
    Pages 171-208
  9. Marek Capiński, Peter Ekkehard Kopp
    Pages 209-217
  10. Marek Capiński, Peter Ekkehard Kopp
    Pages 219-221
  11. Back Matter
    Pages 223-227

About this book

Introduction

The central concepts in this book are Lebesgue measure and the Lebesgue integral. Their role as standard fare in UK undergraduate mathematics courses is not wholly secure; yet they provide the principal model for the development of the abstract measure spaces which underpin modern probability theory, while the Lebesgue function spaces remain the main sour ce of examples on which to test the methods of functional analysis and its many applications, such as Fourier analysis and the theory of partial differential equations. It follows that not only budding analysts have need of a clear understanding of the construction and properties of measures and integrals, but also that those who wish to contribute seriously to the applications of analytical methods in a wide variety of areas of mathematics, physics, electronics, engineering and, most recently, finance, need to study the underlying theory with some care. We have found remarkably few texts in the current literature which aim explicitly to provide for these needs, at a level accessible to current under­ graduates. There are many good books on modern prob ability theory, and increasingly they recognize the need for a strong grounding in the tools we develop in this book, but all too often the treatment is either too advanced for an undergraduate audience or else somewhat perfunctory.

Keywords

Analysis Integration Measure theory Measure-theoretic probability Random variable calculus function probability probability distribution probability theory theorem variable

Authors and affiliations

  • Marek Capiński
    • 1
  • Peter Ekkehard Kopp
    • 2
  1. 1.Nowy Sacz Graduate School of BusinessNowy SaczPoland
  2. 2.Department of MathematicsUniversity of HullHullUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3631-6
  • Copyright Information Springer-Verlag London 1999
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-76260-7
  • Online ISBN 978-1-4471-3631-6
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site