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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 31 mm
Gewicht
ISBN-13
978-0-471-59518-2 (9780471595182)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Ole A. Nielsen is the author of An Introduction to Integration and Measure Theory, published by Wiley.
Autor*in
Queen's University at Kingston, Ontario, Canada
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.
