Integral, Measure and Derivative - G. E. Shilov
| Автор: | G. E. Shilov |
| Издательство: | Ingram |
| Серия: | Dover Books on Mathematics |
| Жанр произведения: | Математика |
| Год издания: | 0 |
| isbn: | 9780486165615 |
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.