Measuring the probabilistic powerdomain

Authors:
Keye Martin;Michael Mislove;James Worrell
Affiliations:
Programming Research Group, Wolfson Building, Oxford University, Oxford, OX1 3PG, UK;Department of Mathematics, Tulane University, New Orleans, LA;Department of Mathematics, Tulane University, New Orleans, LA
Venue:
Theoretical Computer Science - Special issue on automata, languages and programming
Year:
2004

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Abstract

In this paper we initiate the study of measurements on the probabilistic powerdomain. We show how measurements on an underlying domain naturally extend to its probabilistic powerdomain, so that the kernel of the extension consists of exactly those normalized measures on the kernel of the measurement on the underlying domain. This result is combined with now-standard results from the theory of measurements to obtain a new proof that the fixed point associated with a weakly hyperbolic IFS with probabilities is the unique invariant measure whose support is the attractor of the underlying IFS.