Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition.

Introductory Real Analysis

A. N. Kolmogorov

PRENTICE/HALL

English translation by K.L. Chung,revised 1968

Limit Distributions for Sums of Independent Random Variables

B.V. Gnedenko

Addison-Wesley

Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow. Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks. Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.

Elements of the Theory of Functions and Functional Analysis (Dover Books on Mathematics)

Science & Math

S. V. Fomin

Mathematics

Dover Publications

This volume in Richard Silverman's exceptional series of translations of Russian works in the mathematical science is a comprehensive, elementary introduction to real and functional analysis by two faculty members from Moscow University. It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus. The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched. With these problems and the clear exposition, this book is useful for self-study or for the classroom — it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.

Introductory Real Analysis (Dover Books on Mathematics)

Foundations of the Theory of Probability (AMS Chelsea Publishing)

American Mathematical Society

Intended for anyone who wants a thorough understanding of modern statistics, this basic tract develops probability theory on a postulational basis. The book is intended for graduate students and research mathematicians.

Foundations of the Theory of Probability

Chelsea Pub. Co

2021 Reprint of the 1954 Edition. Facsimile of the original edition and not reproduced with Optical Recognition. This treatise on the fundamental limit theorems in probability theory is strong on mathematical rigor, but the presentation is equally distinguished by clarity and elegance. With broad perspectives on the development from the law of large numbers (Bernoulli, 1713) and the limit theorems of de Moivre (1730), Laplace (1812), and Poisson (1837), over the important progress made by Chebyshev (1867, 1890), Lyapunov (1901), and Lindeberg (1922), the book focuses on the progress experts had made on the subject up to the time of publication. This book may be considered a genuine classic. Of general interest is the material in the two first chapters, which may serve as a basis for any rigorous course in probability theory. The axiomatic foundation of the theory given by Kolmogorov in 1933 is here somewhat modified, the probability distributions being specified so as to form a perfect measure, a restriction which removes certain intricacies, notably in the treatment of conditional probabilities and expectations. The careful translation is based on the Russian original (1949. The two appendixes and some fifty extra footnotes give clarifying and instructive remarks.

Boris V. Gnedenko

Martino Fine Books

Mathematics of the 19th Century: Set of 3 Volumes

Birkhauser

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and integral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and pedagogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.
The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.

Selected Works of A.N. Kolmogorov: vol. 2 Probability Theory and Mathematical Statistics

Reference

Springer

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and integral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and pedagogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.
The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.

Selected Works III: Information Theory and the Theory of Algorithms (Mathematics and its Applications)

See the best price to sell, buy, or rent books by A. N. Kolmogorov. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by A. N. Kolmogorov

See the best price to sell, buy, or rent books by A. N. Kolmogorov. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Introductory Real Analysis

Limit Distributions for Sums of Independent Random Variables

Elements of the Theory of Functions and Functional Analysis (Dover Books on Mathematics)

Introductory Real Analysis (Dover Books on Mathematics)

Foundations of the Theory of Probability (AMS Chelsea Publishing)

Foundations of the Theory of Probability

Limit Distributions for Sums of Independent Random Variables

Mathematics of the 19th Century: Set of 3 Volumes

Selected Works of A.N. Kolmogorov: vol. 2 Probability Theory and Mathematical Statistics

Selected Works III: Information Theory and the Theory of Algorithms (Mathematics and its Applications)