Lebesgue Measure and Integration Theory
Foundations and Solved Exercises
- 1st Edition - March 23, 2026
- Latest edition
- Authors: Alberto Cabada, Francisco Javier Fernández
- Language: English
Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for studen… Read more
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Description
Description
Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for students of mathematics and physics. This book provides the complete theoretical underpinnings of this theory, with the corresponding proofs, adapted to the level of advanced undergraduate and graduate students in these disciplines. Beginning with a fundamental discussion of measure spaces, the book moves onto measurable and non-measurable sets, approximation of measurable sets, measurable functions, the Lebesgue integral, the relationship between differentiation and integration on R, and product measures, among other topics. Examples and solved exercises are included across chapters to reinforce understanding and application.
Key features
Key features
- Provides a thorough, engaging discussion of Lebesgue measure and integration theory for students of mathematics and physics
- Highlights different aspects of measure theory, and places special emphasis on the existence of non-measurable sets and notable examples
- Considers measurable and non-measurable sets, measurable functions, generation of measure spaces, the Lebesgue-Stieltjes measure space in R and Rn, and product measures, among other topics
- Includes proofs, examples, and solved exercises across all chapters
Readership
Readership
Advanced undergraduate, graduate, and PhD mathematics and physics students
Table of contents
Table of contents
1 Measure spaces and Lebesgue measure
2. Measurable functions
3. The Lebesgue Integral
4. The Relationship between Differentiation and Integration on R
5. Product measures
2. Measurable functions
3. The Lebesgue Integral
4. The Relationship between Differentiation and Integration on R
5. Product measures
Product details
Product details
- Edition: 1
- Latest edition
- Published: March 23, 2026
- Language: English
About the authors
About the authors
AC
Alberto Cabada
Alberto Cabada is Professor at the University of Santiago de Compostela (Spain). His line of research is devoted to the existence and multiplicity of solutions of nonlinear differential equations, both ordinary and partial, as well as difference and fractional ones. He is the author of more than one hundred forty research and has authored two monographs.
Affiliations and expertise
Department of Mathematical Analysis, Faculty of Mathematics, Universidade de Santiago de Compostela, SpainFF
Francisco Javier Fernández
Francisco Javier Fernández is Associate Professor at the University of Santiago de Compostela. He has participated in 8 national and regional research projects and is the author of 27 research publications. He has also participated in 27 national and international conferences. Francisco Javier Fernández has received 3 consecutive teaching merit awards, the last of these for the period of 2016-2021. Since the beginning of his academic career at the University of Santiago de Compostela, he has taught subjects related to measurement theory and Lebesgue integration.
Affiliations and expertise
Associate Professor, University of Santiago de Compostela,, Spain