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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics) - Tapa dura
Sinopsis
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.
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Críticas
." . .well written and authoritative." ---Choice "The style is characterized by its clarity and concreteness. . . . this work constitutes an excellent introductory textbook for those who wish to get acquainted with the modern methods of real variables." ---Mathematical Reviews
Reseña del editor
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.
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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)
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Measure and Integral: An Introduction to Real Analysis
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Marcel Dekker, Inc, 1977
ISBN 10: 0824764994
ISBN 13: 9780824764999
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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)
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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)
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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)
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