The Resource Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov
Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov
 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
 Language
 eng
 Extent
 xix, 772 pages
 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 RadonNikodym theorem
 12. Integral representation of linear functionals
 13. Appendices
 Isbn
 9781447151210
 Label
 Real analysis : measures, integrals and applications
 Title
 Real analysis
 Title remainder
 measures, integrals and applications
 Statement of responsibility
 Boris Makarov, Anatolii Podkorytov
 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
 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
 Label
 Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov
 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 RadonNikodym 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=ebscotest&password=ebscotest
 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
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/Realanalysismeasuresintegralsand/lGbNNgJHA9A/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/Realanalysismeasuresintegralsand/lGbNNgJHA9A/">Real analysis : measures, integrals and applications, Boris Makarov, Anatolii Podkorytov</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>