Sign-In
Cart
Analysis and Integration Theory: From Riemann to Lebesgue
Hardcover
ISBN13: 9781041408543
Publisher: CRC Press
Published: Dec 16 2026
Pages: 462
Language: English
This book is the culmination of more than two decades of teaching undergraduate and graduate mathematical analysis. It presents a rigorous yet highly accessible treatment of Riemann integration, sequences and series of functions, Fourier series, and measure theory and integration. The exposition emphasizes the development from classical to modern analysis and provides an account of the relationships among different notions of integration and modes of convergence. A central feature of the book is its unified treatment of Riemann and Lebesgue integration within a coherent analytical framework.
The presentation begins with a historical background and proceeds systematically through Riemann integration in one and several variables. This structured progression encourages readers to generalize from Jordan measurable sets to Lebesgue measurable sets, from Jordan measure to Lebesgue measure, and from the Riemann integral to the Lebesgue integral, culminating in three chapters devoted to Lebesgue integration. The treatment of sequences and series of functions stands as a self-contained unit, tracing developments from Euler and Fourier to modern advances.
Key features:
- Rigorous and self-contained development of Riemann integration in R and Rn
- Unified treatment of measure theory and Lebesgue integration
- Coverage of multivariable differentiation, including inverse and implicit function theorems
- Detailed treatment of Fourier series, including pointwise, uniform, and L2 convergence
- Numerous carefully written examples illustrating key results
- Extensive exercises with hints, supported by a separate solutions manual
- Structured teaching plans together with selected final-year project topics and previous examinations.
- This book is aimed at advanced undergraduate and graduate students in mathematics, as well as PhD students and researchers. Combining mathematical rigor with a clear and systematic presentation, this book serves both as a textbook for courses in analysis and integration theory and as a reference for further study in modern mathematics.
This book is aimed at advanced undergraduate and graduate students in mathematics, as well as PhD students and researchers. Combining mathematical rigor with a clear and systematic presentation, this book serves both as a textbook for courses in analysis and integration theory and as a reference for further study in modern mathematics.
Also in
General Mathematics
The Golden Number: Pythagorean Rites and Rhythms in the Development of Western Civilization
Ghyka, Matila C.
Hardcover
How It All Works: All Scientific Laws and Phenomena Illustrated & Demonstrated
Dant, Adam
Clegg, Brian
Hardcover
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Paperback
Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
Leighton, Robert B.
Sands, Matthew
Feynman, Richard P.
Paperback
Oliver Byrne's Elements of Euclid: The First Six Books with Coloured Diagrams and Symbols (Art Meets Science Edition)
Art Meets Science
Hardcover
Math Practice Workbook Grades 6-8: 1000+ Questions You Need to Kill in Middle School by Brain Hunter Prep
Brain Hunter Prep
Paperback
Who Gets What -- And Why: The New Economics of Matchmaking and Market Design
Roth, Alvin E.
Paperback
Tomoko Fuse's Amazing Kusudama Origami: Geometric Paper Art from Japan's Leading Expert!
Fuse, Tomoko
Paperback
The Art of Strategy: A Game Theorist's Guide to Success in Business and Life
Dixit, Avinash K.
Nalebuff, Barry J.
Paperback
Mastering Essential Math Skills Book 2, Bilingual Edition - English/Spanish
Fisher, Richard W.
Paperback
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Hardcover
The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics
Bardi, Jason Socrates
Hardcover
Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter
Orlin, Ben
Hardcover
Counting with - Contando Con Frida (Bilingual: English/Spanish): A Bilingual Counting Book
Stein, Ariana
Rodriguez, Patty
Hardcover
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Shetterly, Margot Lee
Paperback
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology
Sutton, Daud
Lundy, Miranda
Ashton, Anthony
Hardcover
Graph Paper Composition Notebook: Quad Ruled 5x5, Grid Paper for Students in Math and Science
Wizo, Math
Paperback
50 Math Tricks That Will Change Your Life: Mentally Solve the Impossible in Seconds
Zakowich, Tanya
Paperback
New York Post Fiendish Sudoku: The Official Utterly Addictive Number-Placing Puzzle
Gould, Wayne
Paperback
Vector: A Surprising Story of Space, Time, and Mathematical Transformation
Arianrhod, Robyn
Hardcover
Touchthinklearn: Numbers: (Board Books for Baby Learners, Touch Feel Books for Children)
Deneux, Xavier
Hardcover
Quantum Mechanics Done Right: The Shortest Path from Novice to Researcher
Freericks, James K.
Hardcover
ALEKS Math Placement Test Prep 2026: 1200 Verified Practice Questions with Accurate Answer Keys, Step-by-Step Worked Solutions, and Clear Concept Expl
Publishing, Kettford
Reid, Marcus L.
Paperback
A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)
Oakley, Barbara
Paperback
Sudoku for Brain Fitness: 90-Day Challenge to Sharpen the Mind and Strengthen Cognitive Skills
Demyanovich, Julie
Clontz, Steven
Paperback
Un Elefante: Numbers / Números (Bilingual: English/Spanish): A Bilingual Counting Book
Rodriguez, Patty
Stein, Ariana
Hardcover
WorkKeys Study Guide and Practice Test Questions: ACT WorkKeys Exam Prep and Review Book with Applied Mathematics, Locating Information, and Reading f
Trivium Exam Prep Team
Paperback
Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning
Liljedahl, Peter
Paperback
Talentos Ocultos: La Genialidad No Tiene Color. La Fuerza No Tiene Género. El Valor No Tiene Límite.
Shetterly, Margot Lee
Paperback
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks
Shermer, Michael
Benjamin, Arthur
Paperback
Concrete Mathematics: A Foundation for Computer Science
Patashnik, Oren
Knuth, Donald
Graham, Ronald
Hardcover
180 Days(r) Math for First Grade: Practice, Assess, Diagnose
Smith, Jodene Lynn
Smith, Jodene
Paperback
Number Systems and the Foundations of Analysis
Mendelson, Elliott
Dudley, Underwood
Mathematics
Paperback
Medical Dosage Calculations for Dummies
Snyder, Richard W.
Depuente, Vanessa
Schoenborn, Barry
Paperback
The Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science
Schneider, Michael S.
Paperback
Reaching for the Extreme: How the Quest for the Biggest, Fewest, and Weirdest Makes Math
Stewart, Ian
Hardcover
300 Math CrossWords: Addition, Subtraction, Multiplication, and Division Math CrossWords Grade 3 and Above, Age +8
Martin, Josh Ortiz
Paperback
Sciencia: Mathematics, Physics, Chemistry, Biology, and Astronomy for All
Betts, Moff
Tweed, Matt
Watkins, Matthew
Hardcover
Math Fundamentals 3 - Geometry: For Middle School - A Quickstudy Laminated Reference Guide
Expolog
Warren, Peggy
Wright, Susan
Other
Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python
Mirjalili, Vahid
Raschka, Sebastian
Liu, Yuxi (Hayden)
Paperback
It's All a Game: The History of Board Games from Monopoly to Settlers of Catan
Donovan, Tristan
Paperback
30 More Math Mysteries Kids Can't Resist!: Quick & Clever Mysteries That Boost Problem-Solving Skills
Lee, Martin
Paperback