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The Lebesgue-Stieltjes Integral: A Practical Introduction
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Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at advanced undergraduate or graduate level they receive a course on measure and integr… More...

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The Lebesgue-Stieltjes integral : a practical introduction. Undergraduate texts - Carter, Michael and Bruce Van Brunt
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The Lebesgue-Stieltjes integral : a practical introduction. Undergraduate texts - hardcover

2000, ISBN: 9780387950129

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Carter, Michael and Bruce Van Brunt:
The Lebesgue-Stieltjes integral : a practical introduction. Undergraduate texts in mathematics - hardcover

2000

ISBN: 0387950125

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Carter, Michael and Bruce Van Brunt:
The Lebesgue-Stieltjes integral : a practical introduction. Undergraduate texts in mathematics - hardcover

2000, ISBN: 0387950125

gebundene Ausgabe 228 S. Gebundene Ausgabe Das Buch befindet sich in einem ordentlich erhaltenen Zustand. ENGLISCH. Lebesgue-Stieltjes-Integral, Mathematik 3, [PU:New York ; Berlin ; He… More...

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M. Carter:
The Lebesgue-Stieltjes Integral: A Practical Introduction (Undergraduate Texts in Mathematics) - hardcover

2000, ISBN: 0387950125

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Details of the book
The Lebesgue-Stieltjes Integral: A Practical Introduction

While mathematics students generally meet the Riemann integral early in their undergraduate studies, those whose interests lie more in the direction of applied mathematics will probably find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral before they have acquired the necessary theoretical background. This book is aimed at exactly this group of readers. The authors introduce the Lebesgue-Stieltjes integral on the real line as a natural extension of the Riemann integral, making the treatment as practical as possible. They discuss the evaluation of Lebesgue-Stieltjes integrals in detail, as well as the standard convergence theorems, and conclude with a brief discussion of multivariate integrals and surveys of L spaces plus some applications. The whole is rounded off with exercises that extend and illustrate the theory, as well as providing practice in the techniques.

Details of the book - The Lebesgue-Stieltjes Integral: A Practical Introduction


EAN (ISBN-13): 9780387950129
ISBN (ISBN-10): 0387950125
Hardcover
Paperback
Publishing year: 2007
Publisher: Springer-Verlag New York Inc.
244 Pages
Weight: 0,526 kg
Language: eng/Englisch

Book in our database since 2007-06-12T04:42:46-04:00 (New York)
Detail page last modified on 2021-10-06T14:05:39-04:00 (New York)
ISBN/EAN: 9780387950129

ISBN - alternate spelling:
0-387-95012-5, 978-0-387-95012-9


Information from Publisher

Author: M. Carter; B. van Brunt
Title: Undergraduate Texts in Mathematics; The Lebesgue-Stieltjes Integral - A Practical Introduction
Publisher: Springer; Springer US
230 Pages
Publishing year: 2000-05-25
New York; NY; US
Weight: 1,150 kg
Language: English
64,19 € (DE)
65,99 € (AT)
71,00 CHF (CH)
POD

BB; Book; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Fourier series; Lebesgue Theory; Lebesgue-Stieltjes Integral; Riemann integral; calculus; differential equation; differential geometry; measure; B; Analysis; Real Functions; Analysis; Real Functions; Mathematics and Statistics; Reelle Analysis, Real-Variablen; BC; EA

1 Real Numbers.- 1.1 Rational and Irrational Numbers.- 1.2 The Extended Real Number System.- 1.3 Bounds.- 2 Some Analytic Preliminaries.- 2.1 Monotone Sequences.- 2.2 Double Series.- 2.3 One-Sided Limits.- 2.4 Monotone Functions.- 2.5 Step Functions.- 2.6 Positive and Negative Parts of a Function.- 2.7 Bounded Variation and Absolute Continuity.- 3 The Riemann Integral.- 3.1 Definition of the Integral.- 3.2 Improper Integrals.- 3.3 A Nonintegrable Function.- 4 The Lebesgue-Stieltjes Integral.- 4.1 The Measure of an Interval.- 4.2 Probability Measures.- 4.3 Simple Sets.- 4.5 Definition of the Integral.- 4.6 The Lebesgue Integral.- 5 Properties of the Integral.- 5.1 Basic Properties.- 5.2 Null Functions and Null Sets.- 5.3 Convergence Theorems.- 5.4 Extensions of the Theory.- 6 Integral Calculus.- 6.1 Evaluation of Integrals.- 6.2 IWo Theorems of Integral Calculus.- 6.3 Integration and Differentiation.- 7 Double and Repeated Integrals.- 7.1 Measure of a Rectangle.- 7.2 Simple Sets and Simple Functions in Two Dimensions.- 7.3 The Lebesgue-Stieltjes Double Integral.- 7.4 Repeated Integrals and Fubini’s Theorem.- 8 The Lebesgue SpacesLp.- 8.1 Normed Spaces.- 8.2 Banach Spaces.- 8.3 Completion of Spaces.- 8.4 The SpaceL1.- 8.5 The LebesgueLp.- 8.6 Separable Spaces.- 8.7 ComplexLpSpaces.- 8.8 The Hardy SpacesHp.- 8.9 Sobolev SpacesWk,p.- 9 Hilbert Spaces andL2.- 9.1 Hilbert Spaces.- 9.2 Orthogonal Sets.- 9.3 Classical Fourier Series.- 9.4 The Sturm-Liouville Problem.- 9.5 Other Bases forL2.- 10 Epilogue.- 10.1 Generalizations of the Lebesgue Integral.- 10.2 Riemann Strikes Back.- 10.3 Further Reading.- Appendix: Hints and Answers to Selected Exercises.- References.
The book introduces the Lebesgue-Stieltjes integral on the real line in a natural way as an extension of the Riemann integral. Many applied mathematicians will in all probability find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral without having the necessary theoretical background. It is to such readers that this book is addressed. Exercises which extend and illustrate the theory, and provide practice in techniques, are included.

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