Projective topology on bifinite domains and applications

Samy Abbes (1) , Klaus Keimel (2)

1 PPS - Preuves, Programmes et Systèmes
2 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt

We revisit extension results from continuous valuations to Radon measures for bifinite domains. In the framework of bifinite domains, the Prokhorov theorem (existence of projective limits of Radon measures) appears as a natural tool, and helps building a bridge between Measure theory and Domain theory. The study we present also fills a gap in the literature concerning the coincidence between projective and Lawson topology for bifinite domains. Motivated by probabilistic considerations, we study the extension of measures in order to define Borel measures on the space of maximal elements of a bifinite domain.

Mots clés: Bifinite domains; Continuous valuations; Radon measures; Maximal elements

Domaines: Réseaux et télécommunications [cs.NI]

Samy Abbes, Klaus Keimel. Projective topology on bifinite domains and applications. Theoretical Computer Science, 2006, 365 (3), pp.171-183. ⟨10.1016/j.tcs.2006.07.047⟩. ⟨hal-00350211⟩