Elements of the Theory of Functions and Functional Analysis [Two Volumes in One]

by A.N. Kolmogorov

2012 Reprint of Volumes One and Two, 1957-1961. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. A. N. Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, logic, turbulence, classical mechanics and computational complexity. Later in life Kolmogorov changed his research interests to the area of turbulence, where his publications beginning in 1941 had a significant influence on the field. In classical mechanics, he is best known for the Kolmogorov-Arnold-Moser theorem. In 1957 he solved a particular interpretation of Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time. Based on the authors' courses and lectures, this two-part advanced-level text is now available in a single volume. Topics include metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, and more. Each section contains exercises. Lists of symbols, definitions, and theorems.

Genres: Mathematics, Reference, Functional Analysis, Science, Textbooks

278 pages, Paperback

First published January 1, 1954

About the author

Dr. Andrey Nikolaevich Kolmogorov, Ph.D. (Moscow State University, 1929; Russian: Андре́й Никола́евич Колмого́ров) was a Soviet mathematician and professor at the Moscow State University where he became the first chairman of the department of probability theory two years after the 1933 publication of his book which laid the modern axiomatic foundations of the field. He was a Member of the Russian Academy of Sciences and winner of many awards, including the Stalin Prize (1941), the Lenin Prize (1965), the Wolf Prize (1980), and the Lobachevsky Prize (1986).

Reviews

[sarah · Rating 5 out of 5]

This book is actually quite funny in places. I never expected to smile and laugh while reading a functional analysis book. Nicely done.

[Jonah Marcus · Rating 5 out of 5]

Kolmogorov gets a big wet smooch from me 😫🥵💏😫💃🕺🤸🥵

[Nick Black]

ugh i hope i'm still young enough to learn things like this

[Pietro · Rating 4 out of 5]

Good introductory text; gives excellent examples of the abstract concepts introduced. The proofs are nice, and the motivation is adequate, but most exercises are too easy.

[Sarah · Rating 5 out of 5]

This book is actually quite funny in places. I never expected to smile and laugh while reading a functional analysis book. Nicely done.