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