Skip to main content
SpringerLink
Log in

Problems in Analysis

  • Textbook
  • © 1982

Overview

Authors:
  1. Bernard R. Gelbaum

    1. Department of Mathematics, State University of New York, Buffalo, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Problem Books in Mathematics (PBM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (30 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Problems

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Set Algebra

      • Bernard R. Gelbaum
      Pages 3-4

    3. Topology

      • Bernard R. Gelbaum
      Pages 5-7

    4. Limits

      • Bernard R. Gelbaum
      Pages 8-9

    5. Continuous Functions

      • Bernard R. Gelbaum
      Pages 10-14

    6. Functions from ℝn to ℝm

      • Bernard R. Gelbaum
      Pages 15-19

    7. Measure and Topology

      • Bernard R. Gelbaum
      Pages 20-22

    8. General Measure Theory

      • Bernard R. Gelbaum
      Pages 23-27

    9. Measures in ℝn

      • Bernard R. Gelbaum
      Pages 28-30

    10. Lebesgue Measure in ℝn

      • Bernard R. Gelbaum
      Pages 31-34

    11. Lebesgue Measurable Functions

      • Bernard R. Gelbaum
      Pages 35-37

    12. L1 (X, μ)

      • Bernard R. Gelbaum
      Pages 38-42

    13. L2 (X, μ) or ℌ (Hilbert Space)

      • Bernard R. Gelbaum
      Pages 43-46

    14. Lp (X, μ), 1 ≦ p ≦ ∞

      • Bernard R. Gelbaum
      Pages 47-48

    15. Topological Vector Spaces

      • Bernard R. Gelbaum
      Pages 49-54

    16. Miscellaneous Problems

      • Bernard R. Gelbaum
      Pages 55-64

  3. Solutions

    1. Front Matter

      Pages 65-65
      Download chapter PDF

    2. Set Algebra

      • Bernard R. Gelbaum
      Pages 67-68

    3. Topology

      • Bernard R. Gelbaum
      Pages 69-75
Back to top

Keywords

About this book

These problems and solutions are offered to students of mathematics who have learned real analysis, measure theory, elementary topology and some theory of topological vector spaces. The current widely used texts in these subjects provide the background for the understanding of the problems and the finding of their solutions. In the bibliography the reader will find listed a number of books from which the necessary working vocabulary and techniques can be acquired. Thus it is assumed that terms such as topological space, u-ring, metric, measurable, homeomorphism, etc., and groups of symbols such as AnB, x EX, f: IR 3 X 1-+ X 2 - 1, etc., are familiar to the reader. They are used without introductory definition or explanation. Nevertheless, the index provides definitions of some terms and symbols that might prove puzzling. Most terms and symbols peculiar to the book are explained in the various introductory paragraphs titled Conventions. Occasionally definitions and symbols are introduced and explained within statements of problems or solutions. Although some solutions are complete, others are designed to be sketchy and thereby to give their readers an opportunity to exercise their skill and imagination. Numbers written in boldface inside square brackets refer to the bib­ liography. I should like to thank Professor P. R. Halmos for the opportunity to discuss with him a variety of technical, stylistic, and mathematical questions that arose in the writing of this book. Buffalo, NY B.R.G.

Authors and Affiliations

  • Department of Mathematics, State University of New York, Buffalo, USA

    Bernard R. Gelbaum

Bibliographic Information

  • Book Title: Problems in Analysis

  • Authors: Bernard R. Gelbaum

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4615-7679-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-1-4615-7681-5Published: 12 December 2012

  • eBook ISBN: 978-1-4615-7679-2Published: 06 December 2012

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: VIII, 228

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation