Integral, Measure and Derivative

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 feature [...]
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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. "e;The exposition is fresh and sophisticated,"e; declared Sci-Tech Book News, "e;and will engage the interest of accomplished mathematicians."e; Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory, and obtaining the "e;classical"e; 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.