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20140310151446.0 |
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020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
International Standard Book Number |
9781447151227 |
|
978-1-4471-5122-7 |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
Classification number |
QA312-312.5 |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
Classification number |
515.42 |
Edition number |
23 |
264 #1 - |
-- |
London : |
-- |
Springer London : |
-- |
Imprint: Springer, |
-- |
2013. |
912 ## - |
-- |
ZDB-2-SMA |
100 1# - MAIN ENTRY--PERSONAL NAME |
Personal name |
Makarov, Boris. |
Relator term |
author. |
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
Title |
Real Analysis: Measures, Integrals and Applications |
Medium |
[electronic resource] / |
Statement of responsibility, etc |
by Boris Makarov, Anatolii Podkorytov. |
300 ## - PHYSICAL DESCRIPTION |
Extent |
XIX, 772 p. 23 illus. |
Other physical details |
online resource. |
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
Title |
Universitext, |
International Standard Serial Number |
0172-5939 |
505 0# - FORMATTED CONTENTS NOTE |
Formatted contents note |
Measure -- The Lebesgue Model -- Measurable Functions -- The Integral -- The Product Measure -- Change of Variables in an Integral -- Integrals Dependent on a Parameter -- Surface Integrals -- Approximation and Convolution of the Space -- Fourier Series and the Fourier Transform -- Charges. The Radon-Nikodym Theory -- Integral Representation of Linear Functionals -- Appendices. |
520 ## - SUMMARY, ETC. |
Summary, etc |
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. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Fourier analysis. |
|
Topical term or geographic name as entry element |
Geometry. |
|
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Measure and Integration. |
|
Topical term or geographic name as entry element |
Fourier Analysis. |
|
Topical term or geographic name as entry element |
Real Functions. |
|
Topical term or geographic name as entry element |
Geometry. |
700 1# - ADDED ENTRY--PERSONAL NAME |
Personal name |
Podkorytov, Anatolii. |
Relator term |
author. |
710 2# - ADDED ENTRY--CORPORATE NAME |
Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY |
Title |
Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
Display text |
Printed edition: |
International Standard Book Number |
9781447151210 |
856 40 - ELECTRONIC LOCATION AND ACCESS |
Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-4471-5122-7 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) |
Source of classification or shelving scheme |
|
Item type |
E-Book |