Measure and Integral An Introduction to Real Analysis
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Description: This volume develops the classical theory of the Lebesgue integral and some of its applications. Following a thorough study of the concepts of outer measure and measure, the author initially presents the integral in the context of n-dimensional Euclidean space. A more general treatment of the integral, based on an axiomatic approach, is given later. The book examines 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. Several applications of the theory to a specific branch of analysis-harmonic analysis-are also provided.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $94.95
Copyright year: 1977
Publisher: CRC Press LLC
Publication date: 11/1/1977
Size: 6.50" wide x 9.50" long x 0.50" tall
|.. . Preliminaries Points and Sets in Rn|
|Rn as a Metric Space Open and Closed Sets in Rn: Special Sets Compact Sets|
|The Heine-Borel Theorem Functions Continuous Functions and Transformations|
|The Riemann Integral Exercises Function of Bounded Variation|
|The Riemann-Stieltjes Integral Functions of Bounded Variation Rectifiable Curves|
|The Reiman-Stieltjes Integral Further Results About the Reimann-Stieltjes|
|Integrals Exercises Lebesgue Measure and Outer Measure Lebesgue Outer Measures|