Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefully crafted, practical examples. 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.
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, problem-solving, and new areas of research powered by real analysis.
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Table of Contents
1. Abstract Integration2. Construction of Measures
3. Product Measures
4. Complex and Local Measures
5. The Lebesgue-Radon-Nikodym Theorem
6. Measures on Locally Compact Hausdorff Spaces
7. Local Lebesgue-Stieltjes Measures
8. The Fourier Transform
9. Probability
10. Linear ODEs with Measure Coefficients
11. The Boundary Behavior of Holomorphic Functions
12. Appendices
Authors
Ahmed Ghatasheh Assistant Professor of Mathematics, Philadelphia University, Jordan. Ahmed Ghatasheh earned his PhD in Applied Mathematics from the University of Alabama at Birmingham in 2018. He has taught at the Ohio State University and Florida A&M University and currently serves as Assistant Professor of Mathematics at Philadelphia University in Amman, Jordan Steven Redolfi Model Validation Analyst, Regions Financial Corporation, USA. Steven Redolfi earned his PhD in Applied Mathematics from the University of Alabama at Birmingham in 2023. He iscurrently a Model Validation Analyst for Regions Financial Corporation. Rudi Weikard Professor of Mathematics, University of Alabama, Birmingham, USA. Rudi Weikard is Professor of Mathematics at the University of Alabama at Birmingham. He frequently taught the Real Analysis sequence on which this book is modeled. He has authored or coauthored over 70 scholarly papers and coedited three volumes of conference proceedings. Jointly with C. Bennewitz and B.M. Brown, he recently published the book Spectral and Scattering Theory for Ordinary Differential Equations
