Gregory Convertito,David Cruz-Uribe
The Stieltjes Integral
The Stieltjes Integral
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Excellent- More about The Stieltjes Integral
The Stieltjes Integral is a generalization of the Riemann and Darboux integrals of calculus and undergraduate analysis, with applications in number theory, statistics, physics, and finance. This book provides an accessible treatment of the subject for students who have had a one-semester course in analysis, suitable for a second semester course, and for independent study or as the foundation for a senior thesis or Masters project.
Format: Hardback
Length: 250 pages
Publication date: 08 February 2023
Publisher: Taylor & Francis Inc
The Stieltjes Integral is a comprehensive and rigorous treatment of the Stieltjes integral, which is a generalization of the Riemann and Darboux integrals of calculus and undergraduate analysis. This integral serves as a bridge between classical and modern analysis, with applications in various fields such as number theory, statistics, physics, and finance. The book begins with the Darboux integral, builds the theory of functions of bounded variation, and then develops the Stieltjes integral. It culminates with a proof of the Riesz representation theorem as an application of the Stieltjes integral.
For much of the 20th century, the Stjeltjes integral was a standard part of the undergraduate or beginning graduate student sequence in analysis. However, the typical mathematics curriculum has changed at many institutions, and the Stieltjes integral has become less common in undergraduate textbooks and analysis courses. This book seeks to address this by offering an accessible treatment of the subject to students who have had a one-semester course in analysis. The book is suitable for a second semester course in analysis, as well as for independent study or as the foundation for a senior thesis or Masters project.
Features:
1. Written to be rigorous without sacrificing readability.
2. Accessible to undergraduate students who have taken a one-semester course on real analysis.
3. Contains a large number of exercises from routine to challenging.
Dimension: 234 x 156 (mm)
ISBN-13: 9780815374008
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