Integral, Measure and Derivative. G. E. Shilov

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Название: Integral, Measure and Derivative

Автор: G. E. Shilov

Издательство: Ingram

Жанр: Математика

Серия: Dover Books on Mathematics

isbn: 9780486165615

isbn: 0

Аннотация:

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.