# Stochastic order on metric spaces and the ordered Kantorovich monad

@article{Fritz2018StochasticOO, title={Stochastic order on metric spaces and the ordered Kantorovich monad}, author={T. Fritz and P. Perrone}, journal={ArXiv}, year={2018}, volume={abs/1808.09898} }

In earlier work, we had introduced the Kantorovich probability monad on complete metric spaces, extending a construction due to van Breugel. Here we extend the Kantorovich monad further to a certain class of ordered metric spaces, by endowing the spaces of probability measures with the usual stochastic order. It can be considered a metric analogue of the probabilistic powerdomain.
The spaces we consider, which we call L-ordered, are spaces where the order satisfies a mild compatibility… CONTINUE READING

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