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Invitation to real analysis. (English) Zbl 1448.26003

Pure and Applied Undergraduate Texts 36. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4928-5/hbk; 978-1-4704-5233-9/ebook). x, 303 p. (2019).
A textbook covering introductory parts of real analysis – necessary prerequisites (logic, sets, functions, methods of proofs), some metric and topological properties of the real line, sequences and their limits, continuity and differentiability of real functions, their integration, function sequences and series. The propositions are accompanied by detailed proofs and illustrative examples, what makes the text suitable also for independent study. Sections are followed by sets of problems, ranking from routine to almost nontrivial.

MSC:

26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
26A03 Foundations: limits and generalizations, elementary topology of the line
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
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