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We describe a mathematical structure that can give extensional denotationalsemantics to higher-order probabilistic programs. It is not limited to discreteprobabilities, and it is compatible with integration in a way the models thathave been proposed before are not. It is organised as a model of propositionallinear logic in which all the connectives have intuitive probabilisticinterpretations. In addition, it has least fixed points for all maps, so it caninterpret recursion.

Extensional Denotational Semantics of Higher-Order Probabilistic Programs, Beyond the Discrete Case