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Selected Problems in Real Analysis
B. M. Makarov, M. G. Goluzina, A. A. Lodkin, and A. N. Podkorytov, Saint Petersburg State University, St. Petersburg, Russia
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Translations of Mathematical Monographs
1992; 370 pp; softcover
Volume: 107
Reprint/Revision History:
reprinted 1998
ISBN-10: 0-8218-0953-9
ISBN-13: 978-0-8218-0953-2
List Price: US$121
Member Price: US$96.80
Order Code: MMONO/107.S
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This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore.

Readership

Graduate students as well as experts in theoretical and mathematical physics, differential and integral equations and mathematical analysis.

Reviews

"This book is full of marvels ... For teacher, for the researcher, this book will prove a priceless resource ... an energizer of one's research efforts, an avenue to new and often surprising ideas ... physically beautiful and elegantly printed."

-- The Mathematical Intelligencer

"This book should be very useful to teachers and students who seek some challenging problems in real analysis."

-- Mathematical Reviews

Table of Contents

  • Introduction
  • Sequences
  • Functions
  • Series
  • Integrals
  • Asymptotics
  • Functions (continuation)
  • Lebesgue measure and the Lebesgue integral
  • Sequences of measurable functions
  • Iterates of transformations of an interval
  • Answers
  • Appendix I-III
  • Bibliography
  • Subject index
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