Accession Number : AD0778371

Title :   An Analysis of the Daniell and McShane Theories of Integration.

Descriptive Note : Master's thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING

Personal Author(s) : Riley,William J.

Report Date : DEC 1973

Pagination or Media Count : 128

Abstract : The second chapter of the thesis concerns the development of a theory of integration based upon the Daniell integral. The Daniell integral is defined on an initial class of functions and then extended to include a larger class of functions. Important properties of the Daniell integral and the class of functions upon which the Daniell integral acts are proven. The equivalence of a suitably restricted Daniell integral and the Lebesgue integral is demonstrated. Finally, a generalization of the Daniell integral, the Daniell-Stieltjes integral, is developed and the relation between the Daniell-Stieltjes and the Lebesgue-Stieltjes integrals is shown. In Chapter III the theory of the McShane integral is developed. The equivalence of the McShane and Lebesgue integrals is proven. (Modified author abstract)

Descriptors :   *Integral equations, *Numerical integration, Functions(Mathematics), Vector spaces, Convergence, Theorems, Theses

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE