Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.
Measurable functions; Measures; The integral; Integrable functions; The lebesgue spaces; Modes of convergence; Decomposition of measures; Generation of measures; Product measures.
The Elements of Integration and Lebesgue Measure
Multiple integrals and the Stieltjes integral are also examined. This book will be of interest to mathematicians and students taking pure and applied mathematics.
"'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply ...
Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.
Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration.
This volume develops the classical theory of the Lebesgue integral and some of its applications.
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis.
This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject.
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