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Elsevier

Measure and Integration

Concepts, Examples, and Applications

  • 1 Edición - 7 de enero de 2026
  • Última edición
  • Autores: Ahmed Ghatasheh, Steven Redolfi, Rudi Weikard
  • Idioma: Inglés

Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefu… Leer más

Descripción

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.

Puntos claves

  • 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

De interès para

Junior and Senior level undergraduate or early graduate level mathematics students

Índice

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

Detalles del producto

  • Edición: 1
  • Última edición
  • Publicado: 7 de enero de 2026
  • Idioma: Inglés

Sobre los autores

AG

Ahmed Ghatasheh

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

Afiliaciones y experiencia
Assistant Professor of Mathematics, Philadelphia University, Jordan

SR

Steven Redolfi

Steven Redolfi earned his PhD in Applied Mathematics from the University of Alabama at Birmingham in 2023. He is currently a Model Validation Analyst for Regions Financial Corporation.
Afiliaciones y experiencia
Model Validation Analyst, Regions Financial Corporation, USA

RW

Rudi Weikard

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
Afiliaciones y experiencia
Professor of Mathematics, University of Alabama, Birmingham, USA

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