---

＜電子ブック＞
Real Analysis: Measures, Integrals and Applications / by Boris Makarov, Anatolii Podkorytov
(Universitext. ISSN:21916675)

版	1st ed. 2013.
出版者	(London : Springer London : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XIX, 772 p. 23 illus : online resource
著者標目	*Makarov, Boris author Podkorytov, Anatolii author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Fourier analysis LCSH:Functions of real variables LCSH:Geometry FREE:Measure and Integration FREE:Fourier Analysis FREE:Real Functions FREE:Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4471-5122-7

 類似資料