Measure and Integration
Concepts, Examples, and Applications
- 1st Edition - April 1, 2026
- Latest edition
- Authors: Rudi Weikard, Steven Redolfi, Ahmed Ghatasheh
- Language: English
Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefu… Read more
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. Advanced exercises are also included at the end of each chapter, with exercise difficulty level noted for instructors, and solutions included in an appendix.
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.
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.
- Applies real analysis-based problem solving across a range of mathematical topics, from product spaces to radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among others
- Reinforces understanding of core concepts, proofs, and theorems of real analysis to encourage independent thinking
- Features additional exercises at the end of each chapter and solutions in an appendix
Junior and Senior level undergraduate or early graduate level mathematics students
1. Abstract Integration
2. 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
2. 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
- Edition: 1
- Latest edition
- Published: April 1, 2026
- Language: English
RW
Rudi Weikard
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.
Affiliations and expertise
Professor of Mathematics, University of Alabama, Birmingham, USASR
Steven Redolfi
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.
Affiliations and expertise
Model Validation Analyst, Regions Financial Corporation, USAAG
Ahmed Ghatasheh
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.
Affiliations and expertise
Assistant Professor of Mathematics, Philadelphia University, Jordan