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Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics)



Rok: 1977
ISBN: 9780824764999
OKCZID: 110086879

Citace (dle ČSN ISO 690):
WHEEDEN, Richard L. Measure and integral: an introduction to real analysis. New York: Dekker, c1977. x, 274 s. Monographs and textbooks in pure and applied mathematics, 43.

Hodnocení: 4.0 / 5 (6 hlasů)


Anotace

 

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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