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Guides undergraduate students from calculus to measure theory and the Lebesgue integral
Provides a self-contained presentation of metric spaces and their topology tailored for first-time students of real analysis
Includes cumulative exercises that prepare students for real analysis’s many applications
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuity on metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral.
Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.
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Authors and Affiliations
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Department of Mathematics, University of Colorado, Colorado Springs, USA
Rinaldo B. Schinazi
About the author
Bibliographic Information
Book Title: From Classical to Modern Analysis
Authors: Rinaldo B. Schinazi
DOI: https://doi.org/10.1007/978-3-319-94583-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-94582-8Published: 04 October 2018
Softcover ISBN: 978-3-030-06879-0Published: 03 January 2019
eBook ISBN: 978-3-319-94583-5Published: 21 September 2018
Edition Number: 1
Number of Pages: XII, 270
Number of Illustrations: 1 b/w illustrations
Topics: Functional Analysis, Real Functions, Measure and Integration