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Theory of Functions of a Real Variable, Vol. I by I.P.Natanson

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Theory of Functions of a Real Variable, Vol. I written by I.P.Natanson . Translated from Russina by Leo F Boron , Department of Mathematics, University of Michigan. With the editorial collaboration of, and with annotations by Edwin Hewitt, Professor of Mathematics, University of Washington. This book treats the theory of functions of a real variable from a largely classical point of view. It is designed for use in the current Soviet Universty Program, by students in their third year of university studies. The author is a distinguished Soviet sientist and teacher, who has evidently lectured for a number of years on the subject matter of present book. The book has been through two earlier editions, one in 1941 under the title Foundation of the Theory of Functions of a Real Variable and a second in the Ukrainian language, with various extensions by S. I. Zuhovichii. This book cover the following topics.

Theory of Functions of a Real Variable, Vol. I written by I.P.Natanson cover the following topics.

  • 1. Infinite Sets
    2. Point Sets
    3. Measure Sets
    4. Measurable Functions
    5. The Lebesgue Integral of a Bounded Function
    6. Summable Functions
    7. Square Summable Functions
    8. Functions of Finite Variation. The Stieltjes Integral
    9. Absolutely Continous Fuctions. The Indefinite Lebesgue Integral

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