Skip to content
Register Sign in Wishlist
Geometry of Sets and Measures in Euclidean Spaces

Geometry of Sets and Measures in Euclidean Spaces
Fractals and Rectifiability

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 1999
  • availability: Available
  • format: Paperback
  • isbn: 9780521655958

Paperback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

    • Geometric measure theory is a subject now in vogue
    • Author is an authority in the field
    • Explains the analytical mathematics behind fractals
    Read more

    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: February 1999
    • format: Paperback
    • isbn: 9780521655958
    • length: 356 pages
    • dimensions: 226 x 152 x 23 mm
    • weight: 0.52kg
    • availability: Available
  • Table of Contents

    Acknowledgements
    Basic notation
    Introduction
    1. General measure theory
    2. Covering and differentiation
    3. Invariant measures
    4. Hausdorff measures and dimension
    5. Other measures and dimensions
    6. Density theorems for Hausdorff and packing measures
    7. Lipschitz maps
    8. Energies, capacities and subsets of finite measure
    9. Orthogonal projections
    10. Intersections with planes
    11. Local structure of s-dimensional sets and measures
    12. The Fourier transform and its applications
    13. Intersections of general sets
    14. Tangent measures and densities
    15. Rectifiable sets and approximate tangent planes
    16. Rectifiability, weak linear approximation and tangent measures
    17. Rectifiability and densities
    18. Rectifiability and orthogonal projections
    19. Rectifiability and othogonal projections
    19. Rectifiability and analytic capacity in the complex plane
    20. Rectifiability and singular intervals
    References
    List of notation
    Index of terminology.

  • Author

    Pertti Mattila, University of Jyväskylä, Finland

Related Books

also by this author

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.
×