Foundations of Abstract Analysis

Authors: Dshalalow, Eugene

  • Systematic presentation with cutting edge classical themes in point-set topology and measure/integration  
  • Fills a gap between basic and advanced texts through rigorous and yet detailed treatment of topics 
  • Includes solutions to hundreds of problems which help reinforce the text 
  • Key analytical formations preceded by blueprints and discussions 
  • Many historical and biographical inserts on subjects and people
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eBook $69.99
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  • ISBN 978-1-4614-5962-0
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  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4614-5961-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study.

 

While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. 

 

To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. 

Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.

About the authors

Jewgeni H. Dshalalow is a professor at the Florida Institute of Technology, in Melbourne, Florida, USA.

Table of contents (7 chapters)

  • Set-Theoretic and Algebraic Preliminaries

    Dshalalow, Jewgeni H.

    Pages 3-92

  • Analysis of Metric Spaces

    Dshalalow, Jewgeni H.

    Pages 93-169

  • Elements of Point-Set Topology

    Dshalalow, Jewgeni H.

    Pages 171-236

  • Measurable Spaces and Measurable Functions

    Dshalalow, Jewgeni H.

    Pages 239-260

  • Measures

    Dshalalow, Jewgeni H.

    Pages 261-360

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-5962-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4614-5961-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Abstract Analysis
Authors
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4614-5962-0
DOI
10.1007/978-1-4614-5962-0
Hardcover ISBN
978-1-4614-5961-3
Edition Number
2
Number of Pages
XIII, 748
Topics