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Article Dans Une Revue Topology and its Applications Année : 2022

Kantorovich-Rubinstein Quasi-Metrics III: Spaces of Sublinear and Superlinear Previsions

Résumé

Previsions are certain kinds of functionals which model mixtures of probabilistic and non-deterministic choice. For every continuous complete quasimetric X, d, we show that the spaces of (sub)normalized sublinear previsions and of (sub)normalized superlinear previsions on X, with the Kantorovich-Rubinstein quasi-metrics d a KR , are continuous complete. Additionally, the d a KR-Scott topology coincides with the weak topology. If X, d is algebraic complete, then we show that those spaces of previsions are algebraic complete, too, and that finite pointwise suprema (resp., infima) of simple valuations form a strong basis.
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Dates et versions

hal-03787192 , version 1 (24-09-2022)

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Jean Goubault-Larrecq. Kantorovich-Rubinstein Quasi-Metrics III: Spaces of Sublinear and Superlinear Previsions. Topology and its Applications, 2022, pp.108259. ⟨10.1016/j.topol.2022.108259⟩. ⟨hal-03787192⟩
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