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. © 2002 Elsevier B.V. All rights reserved.
Lawson, J. D., & Lu, B. (2003). Riemann and Edalat integration on domains. In Theoretical Computer Science (Vol. 305, pp. 259–275). https://doi.org/10.1016/S0304-3975(02)00696-5