Selected problems in real analysis. Translated from the Russian by H. H. McFaden. (English) Zbl 0765.26001

Translations of Mathematical Monographs. 107. Providence, RI: American Mathematical Society (AMS). x, 370 p. (1992).
The problem book is written primarily for university students and lecturers of mathematics. All facts needed for solutions of the problems are contained in lectures of first two years of university study of mathematics, although many of them are accessible even to first year students.
The book is divided into 10 chapters. First seven chapters deal with classical topics of analysis: sequences, functions, series, integrals, asymptotics. However, problems seem to be more difficult than in usual problem books. Less traditional are Chapters 8-10. They presuppose knowledge of basic concepts of measure theory and by method of combining problems with separate topics into cycles they make the reader familiar with, e.g., Stieltjes integral, \(\varepsilon\)-entropy, Hausdorff dimension and also with elementary notions and results of iteration theory. Brief solutions of problems can be found in the second part of the book.


26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
00A07 Problem books