An Analysis of the Daniell and McShane Theories of Integration.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1973
- Accession Number
- AD0778371
Entities
People
- William J. Riley
Organizations
- Air Force Institute of Technology