Skip to content
Register Sign in Wishlist

Measures, Integrals and Martingales

$56.00 USD

textbook
  • Date Published: December 2007
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511343339

$ 56.00 USD
Adobe eBook Reader

You will be taken to ebooks.com for this purchase
Buy eBook Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259.

    • Introduction to a central mathematical topic accessible for undergraduates
    • Easy to follow exposition with numerous illustrations and exercises included; hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259
    • Text is suitable for classroom use as well as for self-study
    Read more

    Reviews & endorsements

    '... 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

    'This is a concise and elementary introduction to measure and integration theory as need nowadays in many parts of analysis and probability theory.' L'Enseignement Mathématique

    'I have not seen some of the topics that are mentioned above … treated successfully at undergraduate level before, and the book is worth having for these alone … [it] has the potential to revitalize the way that measure theory is taught.' Journal of the Royal Statistical Society

    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

    • Date Published: December 2007
    • format: Adobe eBook Reader
    • isbn: 9780511343339
    • contains: 15 b/w illus. 500 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Prelude
    Dependence chart
    Prologue
    1. The pleasures of counting
    2. sigma-algebras
    3. Measures
    4. Uniqueness of measures
    5. Existance of measures
    6. Measurable mappings
    7. Measurable functions
    8. Integration of positive functions
    9. Integrals of measurable functions and null sets
    10. Convergence theroems and their applications
    11. The function spaces
    12. Product measures and Fubini's theorem
    13. Integrals with respect to image measures
    14. Integrals of images and Jacobi's transformation rule
    15. Uniform integrability and Vitali's convergence theorem
    16. Martingales
    17. Martingale convergence theorems
    18. The Radon-Nikodym theorem and other applications of martingales
    19. Inner product spaces
    20. Hilbert space
    21. Conditional expectations in L2
    22. Conditional expectations in Lp
    23. Orthonormal systems and their convergence behaviour
    Appendix A. Lim inf and lim supp
    Appendix B. Some facts from point-set topology
    Appendix C. The volume of a parallelepiped
    Appendix D. Non-measurable sets
    Appendix E. A summary of the Riemann integral
    Further reading
    Bibliography
    Notation index
    Name and subject index.

  • Resources for

    Measures, Integrals and Martingales

    René L. Schilling

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    *This title has one or more locked files and access is given only to lecturers adopting the textbook for their class. We need to enforce this strictly so that solutions are not made available to students. To gain access to locked resources you either need first to sign in or register for an account.


    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

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

  • Author

    René L. Schilling, Technische Universität, Dresden
    Rene Schilling is a Professor of Stochastics at the University of Marburg.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

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 ×

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.
×