Integral Measure and Derivative

Integral Measure and Derivative : A Unified Approach

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This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. "The exposition is fresh and sophisticated," declared "Sci-Tech Book News, " "and will engage the interest of accomplished mathematicians." Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory, and obtaining the "classical" Lebesgue integral in "n" space. Part two constructs the Lebesgue-Stieltjes integral through the Daniell scheme using the Reimann-Stieltjes integral as the elementary integral. Part three develops theory of measure with the general Daniell scheme, and the final part is devoted to the theory of the derivative.

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Product details

  • Paperback | 256 pages
  • 142.24 x 208.28 x 15.24mm | 272.15g
  • Dover Publications Inc.
  • New York, United States
  • English, Russian
  • New edition
  • New edition
  • black & white illustrations
  • 0486635198
  • 9780486635194
  • 422,200

Table of contents

Introduction Part 1 The Integral 1. The Riemann Integral and Step Functions 2. General Theory of the Integral 3. The Lebesgue Integral in n-Space Part 2 The Stieltjes Integral 4. The Riemann-Stieltjes Integral 5. The Lebesgue-Stieltjes Integral 6. Measurable Sets and General Measure Theory 7. Construtive Measure Theory 8. Axiomatic Measure Theory 9. Measure and Set Functions 10. The Derivative of a Set Function Bibliography Index  

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