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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-xv
  2. Marek Capiński, Peter Ekkehard Kopp
    Pages 1-13
  3. Marek Capiński, Peter Ekkehard Kopp
    Pages 15-53
  4. Marek Capiński, Peter Ekkehard Kopp
    Pages 55-74
  5. Marek Capiński, Peter Ekkehard Kopp
    Pages 75-124
  6. Marek Capiński, Peter Ekkehard Kopp
    Pages 125-157
  7. Marek Capiński, Peter Ekkehard Kopp
    Pages 159-186
  8. Marek Capiński, Peter Ekkehard Kopp
    Pages 187-240
  9. Marek Capiński, Peter Ekkehard Kopp
    Pages 241-285
  10. Back Matter
    Pages 287-311

About this book

Introduction

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

Keywords

Analysis Integration Measure theory Measure-theoretic probability Probability calculus conditional probability Integral integration linear optimization Martingal Martingale Mathematica measure measure theory modeling probability probability distribution probability space Random variable

Authors and affiliations

  • Marek Capiński
    • 1
  • Peter Ekkehard Kopp
    • 2
  1. 1.Institute of MathematicsJagiellonian UniversityKrakówPoland
  2. 2.Department of MathematicsUniversity of HullHullUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0645-6
  • Copyright Information Springer-Verlag London 2004
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-781-0
  • Online ISBN 978-1-4471-0645-6
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site