Exercises in Analysis

Part 1

  • Leszek Gasińksi
  • Nikolaos S. Papageorgiou

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

Table of contents

  1. Front Matter
    Pages i-x
  2. Leszek Gasiński, Nikolaos S. Papageorgiou
    Pages 1-191
  3. Leszek Gasiński, Nikolaos S. Papageorgiou
    Pages 193-402
  4. Leszek Gasiński, Nikolaos S. Papageorgiou
    Pages 403-632
  5. Leszek Gasiński, Nikolaos S. Papageorgiou
    Pages 633-834
  6. Leszek Gasiński, Nikolaos S. Papageorgiou
    Pages 835-1004
  7. Back Matter
    Pages 1005-1037

About this book


Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration, and Martingales; measure and topology; and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.


This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.


Martingales functional analysis measure and integration metric spaces stochastic processes topological spaces

Authors and affiliations

  • Leszek Gasińksi
    • 1
  • Nikolaos S. Papageorgiou
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakowPoland
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-06176-4
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-06175-7
  • Online ISBN 978-3-319-06176-4
  • Series Print ISSN 0941-3502
  • About this book