Skip to content
Register Sign in Wishlist

Measures, Integrals and Martingales

2nd Edition

£44.99

textbook
  • Date Published: April 2017
  • availability: Available
  • format: Paperback
  • isbn: 9781316620243

£ 44.99
Paperback

Add to cart Add to wishlist

Other available formats:
eBook


Request inspection copy

Lecturers may request a copy of this title for inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author's webpage at www.motapa.de. This book forms a sister volume to René Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).

    • A very clear exposition which will take the 'fear' out of measure and integration theory
    • Contains clearly structured proofs and numerous exercises designed to deepen understanding of the material
    • Full solutions to all problems are available online, making the text useful for self-study
    Read more

    Reviews & endorsements

    Review of previous edition: '… thorough introduction to a wide variety of first-year graduate-level topics in analysis … accessible to anyone with a strong undergraduate background in calculus, linear algebra and real analysis.' Zentralblatt MATH

    Review of previous edition: 'The author truly covers a wide range of topics … Proofs are written in a very organized and detailed manner … I believe this to be a great book for self-study as well as for course use. The book is ideal for future probabilists as well as statisticians, and can serve as a good introduction for mathematicians interested in measure theory.' Ita Cirovic Donev, MAA Reviews

    Review of previous edition: '… succeeds in handling the technicalities of measure theory, which is traditionally regarded as dry and inaccessible to students (and, I think, the most difficult material that I have taught at undergraduate level) with a light touch. The book is eminently suitable for a course (or two) for good final-year or first-year post-graduate students and has the potential to revitalize the way that measure theory is taught.' N. H. Bingham, Journal of the Royal Statistical Society

    Review of previous edition: 'This book will remain a good reference on the subject for years to come.' Peter Eichelsbacher, Mathematical Reviews

    Review of previous edition: '… this well-written and carefully structured book is an excellent choice for an undergraduate course on measure and integration theory. Most good books on measure and integration are graduate books and, therefore, are not optimal for undergraduate courses … This book is aimed at both (future) analysts and (future) probabilists, and is therefore suitable for students from both these groups.' Filip Lindskog, Journal of the American Statistical Association

    'This book is an admirable counterpart, both to the first author's well-known text Measures, Integrals and Martingales (CUP, 2005/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase, the authors' preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.' Professor N. H. Bingham, Imperial College London

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Edition: 2nd Edition
    • Date Published: April 2017
    • format: Paperback
    • isbn: 9781316620243
    • length: 490 pages
    • dimensions: 247 x 174 x 22 mm
    • weight: 0.97kg
    • contains: 40 b/w illus. 420 exercises
    • availability: Available
  • Table of Contents

    List of symbols
    Prelude
    Dependence chart
    1. Prologue
    2. The pleasures of counting
    3. σ-algebras
    4. Measures
    5. Uniqueness of measures
    6. Existence of measures
    7. Measurable mappings
    8. Measurable functions
    9. Integration of positive functions
    10. Integrals of measurable functions
    11. Null sets and the 'almost everywhere'
    12. Convergence theorems and their applications
    13. The function spaces Lp
    14. Product measures and Fubini's theorem
    15. Integrals with respect to image measures
    16. Jacobi's transformation theorem
    17. Dense and determining sets
    18. Hausdorff measure
    19. The Fourier transform
    20. The Radon–Nikodym theorem
    21. Riesz representation theorems
    22. Uniform integrability and Vitali's convergence theorem
    23. Martingales
    24. Martingale convergence theorems
    25. Martingales in action
    26. Abstract Hilbert spaces
    27. Conditional expectations
    28. Orthonormal systems and their convergence behaviour
    Appendix A. Lim inf and lim sup
    Appendix B. Some facts from topology
    Appendix C. The volume of a parallelepiped
    Appendix D. The integral of complex valued functions
    Appendix E. Measurability of the continuity points of a function
    Appendix F. Vitali's covering theorem
    Appendix G. Non-measurable sets
    Appendix H. Regularity of measures
    Appendix I. A summary of the Riemann integral
    References
    Name and subject index.

  • Resources for

    Measures, Integrals and Martingales

    René L. Schilling

    General Resources

    Lecturer Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact lecturers@cambridge.org.

  • Author

    René L. Schilling, Technische Universität, Dresden
    René L. Schilling is a Professor of Mathematics at Technische Universität, Dresden. His main research area is stochastic analysis and stochastic processes.

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×