An Introduction to Integration and Measure TheoryISBN: 9780471595182
496 pages
January 1997

This book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of RiemannStieltjes integration and deduces the LebesgueStieltjes measure from the LebesgueStieltjes integral.
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LIMITATIONS OF THE RIEMANN INTEGRAL.
Limits of Integrals and Integrability.
Expectations in Probability Theory.
RIEMANNSTIELTJES INTEGRALS.
RiemannStieltjes Integrals: Introduction.
Characterization of RiemannStieltjes Integrability.
Continuous Linear Functionals on C[a,b].
RiemannStieltjes Integrals: Further Properties.
LEBESGUESTIELTJES INTEGRALS.
The Extension of the RiemannStieltjes Integral.
LebesgueStieltjes Integrals.
MEASURE THEORY.
sigmaAlgebras and Algebras of Sets.
Measurable Functions.
Measures.
LebesgueStieltjes 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.
Limits of Integrals and Integrability.
Expectations in Probability Theory.
RIEMANNSTIELTJES INTEGRALS.
RiemannStieltjes Integrals: Introduction.
Characterization of RiemannStieltjes Integrability.
Continuous Linear Functionals on C[a,b].
RiemannStieltjes Integrals: Further Properties.
LEBESGUESTIELTJES INTEGRALS.
The Extension of the RiemannStieltjes Integral.
LebesgueStieltjes Integrals.
MEASURE THEORY.
sigmaAlgebras and Algebras of Sets.
Measurable Functions.
Measures.
LebesgueStieltjes 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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