Gregory Convertito, David Cruz-Uribe

The Stieltjes Integral

• Gebundenes Buch

Produktbeschreibung

This book provides a detailed, rigorous treatment of the Stieltjes integral. It offers an accessible treatment of the subject to students who have had a one semester course in analysis. This book is suitable for a second semester course in analysis, and also for independent study or as the foundation for a senior thesis or Masters project.

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Produktdetails

• Verlag: Taylor & Francis Inc
• Seitenzahl: 250
• Erscheinungstermin: 28. Februar 2023
• Englisch
• Abmessung: 161mm x 241mm x 26mm
• Gewicht: 520g
• ISBN-13: 9780815374008
• ISBN-10: 0815374003
• Artikelnr.: 66268770

Autorenporträt

Gregory Convertito is a Ph.D. candidate in philosophy at DePaul University in Chicago. He attended Trinity College in Hartford, CT as an undergraduate, where he studied both mathematics and philosophy. He then earned an M.A. in philosophy at Boston College. His primary interest is in social and political philosophy and he continues to have an abiding interest in mathematics. David Cruz-Uribe, OFS is a Mexican-American mathematician, born and raised in Green Bay, Wisconsin. He attended the University of Chicago as an undergraduate, and got his PhD at the University of California, Berkeley, under Donald Sarason. After a postdoc at Purdue where he worked with Chris Neugebauer, he joined the faculty of Trinity College, Hartford, teaching there for 19 years. He then moved to the math department at the University of Alabama to become department chair; he wrote this book while serving in this position. His research interests are in harmonic analysis, particularly weighted norm inequalities and variable Lebesgue spaces, and partial differential equations. He is the author and translator of three books in harmonic analysis. He is married with three adult children, and is a professed member of the Secular Franciscan Order.

Inhaltsangabe

1. The Darboux Integral. 1.1. Bounded, Continuous, and Monotonic Functions.
1.2. Step Functions. 1.3. The Darboux Integral. 1.4. Properties of the
Darboux Integral. 1.5. Limits and the Integral. 1.6. The Fundamental
Theorem of Calculus. 1.7. Exercises. 2. Further Properties of the Integral.
2.1. The Lebesgue Criterion. 2.2. The Riemann Integral. 2.3. Integrable
Functions as a Normed Vector Space. 2.4. Exercises. 3. Functions of Bounded
Variation. 3.1. Monotonic Functions. 3.2. Functions of Bounded Variation.
3.3. Properties of Functions of Bounded Variation. 3.4. Limits and Bounded
Variation. 3.5. Discontinuities and the Saltus Decomposition. 3.6. BV [a;
b] as a Normed Vector Space. 3.7. Exercises. 4. The Stieltjes Integral.
4.1. The Stieltjes Integral of Step Functions. 4.2. The Stieltjes Integral
with Increasing Integrator. 4.3. The Stieltjes Integral with BV Integrator.
4.4. Existence of the Stieltjes Integral. 4.5. Limits and the Stieltjes
Integral. 4.6. Exercises. 5. Further Properties of the Stieltjes Integral.
5.1. The Stieltjes Integral and Integration by Parts. 5.2. The
Lebesgue-Stieltjes Criterion. 5.3. The Riemann-Stieltjes Integral. 5.4. The
Riesz Representation Theorem. 5.5. Exercises.