Theory of Functions of a Real Variable by I.P. Natanson (PDF)

Description

Originally published in two volumes, this long out-of-print work by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics, the treatment offers a clear account of integration theory and a practical introduction to functional analysis. Prerequisites include a background in the foundations of elementary analysis and some familiarity with the theory of irrational numbers, the theory of limits, continuous functions, Riemann integrals, and infinite series.Volume I covers infinite and point sets, measurable sets and functions, the Lebesgue integral of a bounded function, square-summable functions, functions of finite variations, the Stieltjes integral, absolutely contiguous functions, and the indefinite Lebesgue integral. Volume II addresses singular integrals, trigonometric series, convex functions, point sets in two-dimensional space, measurable functions of several variables and their integration, set functions and their applications in the theory of integration, transfinite numbers, the Baire classification, certain generalizations of the Lebesgue integral, and some ideas from functional analysis. Many chapters feature challenging exercises.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Ecstatic to receive this Natanson classic from’Better World Books’, published 1961 printed1964. A former library book and in near newcondition.

⭐A clearer, better written exposition of serious mathematics does not exist.I give this book my highest recommendation.

⭐The best book in real variables I ever met. A lot of various information forms a deep understanding of the subject. Some parts may be skipped during the first reading.

⭐Excellent. Does anyone know similar books on the subject ?

⭐Quality of production. Paper quality is VERY poor. See the photograph. The print on the reverse is clearly visible. Dover publications used to be EXCELLENT but sadly those days are GONE as it seems to me.Even if one is prepared to pay for a product, GOOD and QUALITY products are simply NONEXISTENT.Natanson’s book is a timeless classic – NOT some textbook for some course that one simply reads and discards. It is a book that I would like to keep for decades. A better quality production would be desirable.I have purchased literally hundreds of dover books in the bygone decdes butI would STRONGLY hesitate buying dover books in future.

⭐An excellent text by one of the masters of the subject . I was deeply impressed by the clarity of explanation . The approach is classical and it should be read by any one who has some working knowledge of Advanced Calculus ( Real Analysis ). Thank you Dover Publications for reprinting this . I had the Frederic Unger version of the same book ( Hard Cover ) in two separate volumes but the condition was rather poor and hence I got this volume again . To learn mathematics , one should learn it from the masters . I would recomend this to any one who seriously wants to learn the subject .

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