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The Resource Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov

Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov

Label
Real analysis : measures, integrals and applications
Title
Real analysis
Title remainder
measures, integrals and applications
Statement of responsibility
Boris Makarov, Anatolii Podkorytov
Creator
Contributor
Author
Subject
Language
eng
Summary
Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature. This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines the concept of the Hausdorff measure, the properties of the area on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied to harmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables. The book contains more than 600 examples and exercises. The reader who has mastered the first third of the book will be able to study other areas of mathematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory, statistics, functional analysis, partial differential equations and others. Real Analysis: Measures, Integrals and Applications is intended for advanced undergraduate and graduate students in mathematics and physics. It assumes that the reader is familiar with basic linear algebra and differential calculus of functions of several variables. -- page 4 of cover
Member of
Cataloging source
CDX
Illustrations
illustrations
Index
index present
LC call number
QA300
LC item number
.M35 2013
Literary form
non fiction
Nature of contents
bibliography
Series statement
Universitext
Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov
Label
Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov
Publication
Copyright
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Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Measure -- 2. The Lebesgue measure -- 3. Measurable functions -- 4. The integral -- 5. The product measure -- 6. Change of variables in an integral -- 7. Integrals dependent on a parameter -- 8. Surface integrals -- 9. Approximation and convolution in the spaces L[superscript]p -- 10. Fourier series and the Fourier transform -- 11. Charges, the Radon-Nikodym theorem -- 12. Integral representation of linear functionals -- 13. Appendices
http://library.link/vocab/cover_art
https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9781447151210&userID=ebsco-test&password=ebsco-test
Dimensions
24 cm.
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b3504394'}
Extent
xix, 772 pages
Isbn
9781447151210
Isbn Type
(pbk.)
Lccn
2013940613
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
(OCoLC)852197538

Library Locations

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      110 8th St, Troy, NY, 12180, US
      42.729766 -73.682577
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