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More copies of this ISBNOther titles in the Dover Books on Mathematics series:
Integral, Measure and Derivative: A Unified Approach (Dover Books on Mathematics)by G. E. Shilov
Synopses & ReviewsPublisher Comments:This graduatelevel 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 SciTech 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 LebesgueStieltjes integral through the Daniell scheme using the ReimannStieltjes 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. Synopsis:This treatment examines the general theory of the integral, Lebesque integral in n space, the RiemannStieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — SciTech Book News. 1966 edition. Table of ContentsIntroduction Part 1 The Integral 1. The Riemann Integral and Step Functions 2. General Theory of the Integral 3. The Lebesgue Integral in nSpace Part 2 The Stieltjes Integral 4. The RiemannStieltjes Integral 5. The LebesgueStieltjes 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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