
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 WRIGHTPATTERSON 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 DaniellStieltjes integral, is developed and the relation between the DaniellStieltjes and the LebesgueStieltjes 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