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Measure and integral. An introduction to real analysis

Measure and integral. An introduction to real analysis

Richard Wheeden, Antoni Zygmund
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This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.
Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p)) classes, and various results about differentiation are examined in detail. Several applications of the theory to a specific branch of analysis--harmonic analysis--are also provided. Among these applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function.
Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis for student interested in mathematics, statistics, or probability. Requiring only a basic familiarity with advanced calculus, this volume is an excellent textbook for advanced undergraduate or first-year graduate student in these areas.
Categorias:
Ano:
1977
Edição:
1
Editora:
CRC Press
Idioma:
english
Páginas:
287
ISBN 10:
0824764994
ISBN 13:
9780824764999
Série:
Pure and Applied Mathematics
Arquivo:
DJVU, 4.93 MB
IPFS:
CID , CID Blake2b
english, 1977
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