Measure and Integration: Examples, Concepts, and Applications instructs in core proofs, theorems, and approaches of real analysis, as illustrated via compelling exercises and carefully crafted, practical examples. From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking and problem solving, and new areas of research powered by real analysis are introduced. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. Advanced exercises are also included at the end of each chapter, with exercise difficulty level noted for instructors, and solutions included in an appendix.
Sprache
Verlagsort
Verlagsgruppe
Elsevier Science Publishing Co Inc
Zielgruppe
Für höhere Schule und Studium
Maße
Höhe: 235 mm
Breite: 191 mm
ISBN-13
978-0-443-27390-2 (9780443273902)
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Schweitzer Klassifikation
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.
Autor*in
Professor of Mathematics, University of Alabama, Birmingham, UK
Model Validation Analyst, Regions Financial Corporation, USA
Assistant Professor of Mathematics, Philadelphia University, Jordan
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
