Riemann and Edalat integration on domains

Authors:
Jimmie D. Lawson;Bin Lu
Affiliations:
Department of Mathematics, Louisiana State University, Baton Rouge, LA;University of Arizona, Tucson, AZ
Venue:
Theoretical Computer Science - Topology in computer science
Year:
2003

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Abstract

The main result of this paper is that the domain-theoretic approach to the generalized Riemann integral first introduced by Edalat extends to a large class of spaces that can be realized as the set of maximal points of domains.The approach is based on the theory of a Riemann-Stieltjes type integral on a topological space with respect to a finitely additive measure. We develop the theory of this integral for a bounded function f defined on the maximal points of a continuous domain and show that it gives an alternate approach to the Edalat integral.