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

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A. N. Kolmogorov
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Elements of the Theory of Functions and Functional Analysis [Two Volumes in One]

by A. N. Kolmogorov (Author), S.V. Fomin (Author)
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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.
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  1. ISBN-10
    1614273049
  2. ISBN-13
    978-1614273042
  3. Publication date
    May 8, 2012
  4. Language
    English
  5. Dimensions
    6 x 0.7 x 9 inches
  6. Print length
    278 pages
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A. N. Kolmogorov

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Customer reviews

4.7 out of 5 stars
223 global ratings

Top reviews from the United States

  • Aran Joseph Canes
    5.0 out of 5 stars A Mathematical Odyssey
    Reviewed in the United States on April 28, 2018
    Format: PaperbackVerified Purchase
    While it takes some background in higher level mathematics, reading Kolmogorov’s Elements of the Theory of Functions and Functional Analysis is akin to hearing an architect describe the building of Notre Dame or a classicist discuss the Odyssey.

    Beginning with clear definitions, continuing with proofs of theorems and ending in meaningful results like the properties of functions that have a unique derivative or the difference between Lebesgue and Riemann integrals, Kolmogorov wrote a work that allows the collegiate mathematician to catch a glimmer of what supports a vaulted apse or the ring cycles that Homer exploits to full literary effect.

    It’s hard not to overstate how much pleasure a book like this can provide to the mathematically inclined. Yes, mathematics has advanced since Kolmogorov wrote this in 1957 but in terms
    of clarity of thought and language I believe the book to remain a classic. I only wish I could have appreciated how beautiful theoretical mathematics can be when I was in graduate school.

    Highly recommended to those with an intermediate background and interest in higher order mathematics. You are in for one of the great odysseys of the human intellect.
    20 people found this helpful
    Helpful
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  • Chris S. Kopech
    5.0 out of 5 stars Accurate presentation for good price.
    Reviewed in the United States on March 22, 2020
    Format: PaperbackVerified Purchase
    Great content covering an advanced undergraduate collegiate topic for a decently affordable price.
    One person found this helpful
    Helpful
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  • C
    5.0 out of 5 stars I enjoy all textbooks written by Kolmogorov
    Reviewed in the United States on October 10, 2017
    Format: PaperbackVerified Purchase
    I enjoy all textbooks written by Kolmogorov. They are very accessible to beginners like me learning the subject for the first time as he gives lots of intuition behind the theorums/ definitions etc., unlike baby Rudin which has good exercise but is a chore to read (good as reference though).
    6 people found this helpful
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  • Drew L
    5.0 out of 5 stars Five Stars
    Reviewed in the United States on December 22, 2017
    Format: PaperbackVerified Purchase
    Beautifully-written book and made me realize how great of a mathematician Kolmogorov is.
    6 people found this helpful
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  • The Suffocated
    4.0 out of 5 stars A faithful, inexpensive two-volumes-in-one reprint with good print quality
    Reviewed in the United States on October 12, 2019
    Format: PaperbackVerified Purchase
    I will perhaps write a review about this book in the future. Right now I only want to clarify the product details.

    This book, published by Martino Fine Books in 2012, is a faithful, two-volumes-in-one reprint of the English translations of the two volumes of Kolmogorov and Fomin's "Elements of the Theory of Functions and Functional Analysis". The two volumes were translated by Leo F. Boron (volume 1) and Hyman Kamel and Horace Komm (volume 2) from their first (1954 and 1960) Russian editions. The English translations were first published in two volumes (in 1957 and 1961) by Graylock Press, Rochester, New York.

    I was worried at first that this inexpensive (USD 9.5 at the time of writing -- one-third cheaper than the Dover reprint of the same title) republication by a little-known publisher was a scam, but upon delivery, I was glad to find out that this is really a two-volumes-in-one edition with good print quality.
    14 people found this helpful
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  • Marcos Turcio Cuevas
    5.0 out of 5 stars Un libro de Kolmogorov.
    Reviewed in the United States on August 22, 2019
    Format: PaperbackVerified Purchase
    Un libro de análisis concreto y bien estructurado. Fácil de leer y con ejercicios bien pensados.
    2 people found this helpful
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  • 11_bravo_dad
    5.0 out of 5 stars Five Stars
    Reviewed in the United States on July 26, 2018
    Format: PaperbackVerified Purchase
    mind blown
    One person found this helpful
    Helpful
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  • Doug R
    5.0 out of 5 stars Five Stars
    Reviewed in the United States on December 4, 2014
    Format: PaperbackVerified Purchase
    Beautiful republication -- better than the Dover reprint of the same title.
    9 people found this helpful
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Top reviews from other countries

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  • xiucheng
    5.0 out of 5 stars Excellent book
    Reviewed in Singapore on November 9, 2019
    Format: PaperbackVerified Purchase
    This is the masterpiece work. It should be the standard of mathematic books.
    Report
  • MdA
    5.0 out of 5 stars Un clásico maravilloso
    Reviewed in Mexico on May 4, 2022
    Format: PaperbackVerified Purchase
    Un clásico maravilloso. Los autores rusos dando una muestra perfecta de una de las cosas que mejor saben hacer: Matemáticas de alto nivel. Ideal para introducirse al mundo del Análisis Funcional.
    Report
  • Cleber Souza Correa
    5.0 out of 5 stars Excelente
    Reviewed in Brazil on August 11, 2023
    Format: PaperbackVerified Purchase
    Excelente
    Report
  • Rohit
    5.0 out of 5 stars Classic text
    Reviewed in India on January 17, 2025
    Format: PaperbackVerified Purchase
    From one of the greatest mathematician of last 100 years , this book is worth every penny.
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    Rohit
    5.0 out of 5 stars
    Classic text

    Reviewed in India on January 17, 2025
    From one of the greatest mathematician of last 100 years , this book is worth every penny.
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  • Cliente Amazon
    5.0 out of 5 stars Come la versione italiana
    Reviewed in Italy on September 9, 2019
    Format: PaperbackVerified Purchase
    è l'analogo della versione italiana, ma costa molto molto di meno. Sono due libri riuniti in uno. Io l'ho usato per un esame della facoltà di fisica e sinceramente è stato interessantissimo ma non molto utile. Lo consiglio a chi vuole sapere la matematica pura. Non ha molte applicazioni ma spiega molto bene
    Report
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