# The Lebesgue-Stieltjes Integral: A Practical Introduction

## M. Carter; B. Van Brunt

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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.

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Contenuti:

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.

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Book by Carter M Brunt B van

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ISBN 10:  1461270332 ISBN 13:  9781461270331
Casa editrice: Springer Verlag, 2000
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Springer, 2011
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## 1.The Lebesgue-Stieltjes Integral

Editore: Springer-Verlag New York Inc. (2000)
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Descrizione libro Springer-Verlag New York Inc., 2000. HRD. Condizione: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice articolo IQ-9780387950129

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## 2.The Lebesgue-Stieltjes Integral: A Practical Introduction (Hardback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 0387950125 ISBN 13: 9780387950129
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Hardback. Condizione: New. 2000 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. Codice articolo LIE9780387950129

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## 4.The Lebesgue-Stieltjes Integral: A Practical Introduction (Undergraduate Texts in Mathematics)

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## 5.The Lebesgue-Stieltjes Integral: A Practical Introduction (Undergraduate Texts in Mathematics)

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## 6.The Lebesgue-Stieltjes Integral. A Practical Introduction

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## 7.The Lebesgue-Stieltjes Integral: A Practical Introduction (Hardback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 0387950125 ISBN 13: 9780387950129
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Hardback. Condizione: New. 2000 ed.. Language: English . Brand New Book ***** Print on Demand *****. 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. Codice articolo APC9780387950129

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## 8.The Lebesgue-Stieltjes Integral: A Practical Introduction (Hardback)

Editore: Springer-Verlag New York Inc., United States (2000)
ISBN 10: 0387950125 ISBN 13: 9780387950129
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Descrizione libro Springer-Verlag New York Inc., United States, 2000. Hardback. Condizione: New. 2000 ed.. Language: English . Brand New Book ***** Print on Demand *****.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. Codice articolo APC9780387950129

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## 9.The Lebesgue-Stieltjes Integral: A Practical Introduction

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Descrizione libro Springer. Hardcover. Condizione: New. 230 pages. Dimensions: 9.3in. x 6.2in. x 0.8in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Codice articolo 9780387950129

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