Basic Analysis IV: Measure Theory and Integration, 1st Edition (Hardback) book cover

Basic Analysis IV

Measure Theory and Integration, 1st Edition

By James K. Peterson

Chapman and Hall/CRC

499 pages | 13 B/W Illus.

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Hardback: 9781138055117
pub: 2020-05-12
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Description

Basic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides.

Features

• Can be used as a traditional textbook as well as for self-study

• Suitable for advanced students in mathematics and associated disciplines

• Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

Reviews

"Mathematics is fortunate to be populated by bright practitioners. Nonetheless, amongst these we are fortunate to have rare individuals who are wise. Professor Peterson is a member of this distinguished group. His works clearly demonstrate the importance of a long career of research and teaching where he combines the two perspectives of: (1) clearly understanding the needs of diverse readers for clear exposition that scaffolds their exposure to complex material with a transparency about both where they are going and what the utility is of what they are currently reading; and, (2) the benefits of having used the mathematics under consideration in so many diverse applications. The masterly synthesis of so much complex material by a single individual is a superb achievement which will reward serious readers with insight, surprise, and breadth as well as depth."

—Professor John R. Jungck, University of Delaware

Table of Contents

1.Introduction 2.An Overview Of Riemann Integration 3.Functions Of Bounded Variation 4.The Theory Of Riemann Integration 5.Further Riemann Integration Results 6.The Riemann-Stieltjes Integral 7.Further Riemann - Stieljes Results 8.Measurable Functions and Spaces 9.Measure And Integration 10.The Lp Spaces11.Constructing Measures 12.Lebesgue Measure 13.Cantor Set Experiments 14.Lebesgue Stieljes Measure 15.Modes Of Convergence 16. Decomposition Of Measures 17.Connections To Riemann Integration 18.Fubini Type Results 19.Differentiation 20.Summing It All Up. References. Index. Appendix A. Appendix B. Appendix C. Appendix D

About the Author

James Peterson has been an associate professor in the School of Mathematical and Statistical Sciences

since 1990. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2016.

He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages and from first principles analysis of natural phenomena was absolutely essential to make progress.

In both mathematical and applied areas, students often need to use advanced mathematics tools they have not

learned properly. So recently, he has written a series of books on analysis to help researchers with the problem

of learning new things after their degrees are done and they are practicing scientists. Along the way, he has also written papers in immunology, cognitive science and neural network technology in addition to having grants from NSF, NASA and the Army.

He also likes to paint, build furniture and write stories.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT037000
MATHEMATICS / Functional Analysis