Measure and Integration

Concepts, Examples, and Applications

Rudi Weikard, Steven Redolfi, Ahmed Ghatasheh (Autoren)

Buch | Softcover

330 Seiten

2026
Academic Press Inc (Verlag)
978-0-443-27390-2 (ISBN)

Noch nicht erschienen (ca. April 2026)
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Measure and Integration: Examples, Concepts, and Applications offers a comprehensive introduction to the fundamental principles and methods of real analysis, providing readers with a solid foundation through clear explanations, rigorous proofs, and an abundance of thoughtfully constructed exercises. From the very first chapter, students are encouraged to engage actively with concepts, applying them to a range of practical examples that reinforce both understanding and analytical skills. The book’s structured approach ensures that readers not only grasp key theorems and core techniques, but also develop the problem-solving abilities essential for higher-level mathematics and related applications.

The text also delves into advanced areas such as integration on product spaces, Radon functionals, functions of bounded variation, Lebesgue-Stieltjes measures, convolutions, probability, and differential equations. Each chapter concludes with advanced exercises, clearly marked for difficulty, allowing both students and instructors to tailor their study or coursework. An appendix with complete solutions supports independent learning, making the book a valuable resource for both classroom use and self-study.

Rudi Weikard is Professor of Mathematics at the University of Alabama at Birmingham who has frequently taught the Real Analysis sequence. He has authored or co-authored over 60 scholarly articles, co-edited three volumes of conference proceedings, and recently a co-authored (with C. Bennewitz and B.M. Brown) a textbook on Spectral and Scattering Theory for Ordinary Differential Equations. Steven Redolfi graduated with a PhD in Applied Mathematics from the University of Alabama at Birmingham and is currently a Model Validation Analyst for Regions Financial Corporation. He has coauthored papers and given talks on topics which heavily rely on the general integration theory introduced in Real Analysis. Ahmed Ghatasheh graduated with a PhD in Applied Mathematics from the University of Alabama at Birmingham (UAB). After graduation, he taught at The Ohio State University and for Florida A&M University. Currently, he is an assistant professor of mathematics at Philadelphia University in Jordan. During his time at UAB, he coauthored papers and gave talks related to measure and integration theory.

1. Abstract Integration
2. Measures
3. Integration on Product Spaces
4. The Lebesgue-Radon-Nikodym Theorem
5. Radon Functionals on Locally Compact Hausdorff Spaces
6. Differentiation
7. Functions of Bounded Variation and Lebesgue-Stieltjes Measures
8. Convolutions
9. Probability
10. Differential Equations with measure coefficients
11. Appendices

Erscheint lt. Verlag	1.4.2026
Verlagsort	San Diego
Sprache	englisch
Maße	191 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-443-27390-1 / 0443273901
ISBN-13	978-0-443-27390-2 / 9780443273902
Zustand	Neuware