Integral, Measure and Derivative. G. E. Shilov и др.
- Тип: Текст
- Авторы:
- Издательство: Ingram(2020)
- Серия: Dover Books on Mathematics
- ISBN: 9780486165615
- Язык: Английский
- Жанры: Математика
- Описание
- Фрагмент
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.