An Introduction to Integration and Measure Theory / Edition 1

An Introduction to Integration and Measure Theory / Edition 1

by Ole A. Nielsen
     
 

ISBN-10: 0471595187

ISBN-13: 9780471595182

Pub. Date: 01/25/1997

Publisher: Wiley

This book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral.  See more details below

Overview

This book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral.

Product Details

ISBN-13:
9780471595182
Publisher:
Wiley
Publication date:
01/25/1997
Series:
Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts Series, #17
Edition description:
New Edition
Pages:
496
Product dimensions:
6.50(w) x 9.49(h) x 1.10(d)

Table of Contents

LIMITATIONS OF THE RIEMANN INTEGRAL.

Limits of Integrals and Integrability.

Expectations in Probability Theory.

RIEMANN-STIELTJES INTEGRALS.

Riemann-Stieltjes Integrals: Introduction.

Characterization of Riemann-Stieltjes Integrability.

Continuous Linear Functionals on C[a,b].

Riemann-Stieltjes Integrals: Further Properties.

LEBESGUE-STIELTJES INTEGRALS.

The Extension of the Riemann-Stieltjes Integral.

Lebesgue-Stieltjes Integrals.

MEASURE THEORY.

sigma-Algebras and Algebras of Sets.

Measurable Functions.

Measures.

Lebesgue-Stieltjes Measures.

THE ABSTRACT LEBESGUE INTEGRAL.

The Integral Associated with a Measure Space.

The Lebesgue Spaces and Norms.

Absolutely Continuous Measures.

Linear Functionals on the Lebesgue Spaces.

Product Measures and Fubini's Theorem.

Lebesgue Integration and Measures on R^n.

Signed Measures and Complex Measures.

Differentiation.

Convergence of Sequences of Functions.

Measures on Locally Compact Spaces.

Hausdorff Measures and Dimension.

Lorentz Spaces.

Appendices.

Indexes.

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