Principles of Analysis: Measure, Integration, Functional Analysis, and Applications, 1st Edition (Hardback) book cover

Principles of Analysis

Measure, Integration, Functional Analysis, and Applications, 1st Edition

By Hugo D. Junghenn

Chapman and Hall/CRC

520 pages | 23 B/W Illus.

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pub: 2018-04-26
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Description

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers’ benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.

The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part III discusses various advanced topics, building on material covered in the previous parts; Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, the theory of metric spaces and of general topological spaces are covered in detail in a preliminary chapter .

Features:

  • Contains direct and concise proofs with attention to detail
  • Features a substantial variety of interesting and nontrivial examples
  • Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises
  • Provides an eclectic set of special topics and applications

About the Author:

Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.

Table of Contents

Measurable Sets. Measurable Functions. Integration. Further Topics in Measure Theory. Banach Spaces. Hilbert Spaces. Locally Convex Spaces. Banach Algebras. Harmonic Analysis on Locally Compact Groups. Probability Theory. Operator Theory. Appendices.

About the Author

Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics and A Course in Real Analysis. His research interests include functional analysis, semigroups, and probability.

Subject Categories

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