Matches in SemOpenAlex for { <https://semopenalex.org/work/W4299321610> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4299321610 abstract "The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in that case it metrizes the weak topology. We introduce a variant of that construction in the realm of quasi-metric spaces, and prove that it is algebraic Yoneda-complete as soon as the underlying quasi-metric space of points is algebraic Yoneda-complete, and that the associated topology is the weak topology. We do this not only for probability distributions, represented as normalized continuous valuations, but also for subprobability distributions, for various hyperspaces, and in general for different brands of functionals. Those functionals model probabilistic choice, angelic and demonic non-deterministic choice, and their combinations. The mathematics needed for those results are more demanding than in the simpler case of metric spaces. To obtain our results, we prove a few other results that have independent interest, notably: continuous Yoneda-complete spaces are consonant; on a continuous Yoneda-complete space, the Scott topology on the space of $overline{mathbb{R}}_+$-valued lower semicontinuous maps coincides with the compact-open and Isbell topologies, and the subspace topology on spaces of $alpha$-Lipschitz continuous maps also coincides with the topology of pointwise convergence, and is stably compact; we introduce and study the so-called Lipschitz-regular quasi-metric spaces, and we show that the formal ball functor induces a Kock-Zoberlein monad, of which all algebras are Lipschitz-regular; and we prove a minimax theorem where one of the spaces is not compact Hausdorff, but merely compact." @default.
- W4299321610 created "2022-10-02" @default.
- W4299321610 creator A5084807549 @default.
- W4299321610 date "2017-07-12" @default.
- W4299321610 modified "2023-09-29" @default.
- W4299321610 title "Complete Quasi-Metrics for Hyperspaces, Continuous Valuations, and Previsions" @default.
- W4299321610 doi "https://doi.org/10.48550/arxiv.1707.03784" @default.
- W4299321610 hasPublicationYear "2017" @default.
- W4299321610 type Work @default.
- W4299321610 citedByCount "0" @default.
- W4299321610 crossrefType "posted-content" @default.
- W4299321610 hasAuthorship W4299321610A5084807549 @default.
- W4299321610 hasBestOaLocation W42993216101 @default.
- W4299321610 hasConcept C104317684 @default.
- W4299321610 hasConcept C114614502 @default.
- W4299321610 hasConcept C118615104 @default.
- W4299321610 hasConcept C123222754 @default.
- W4299321610 hasConcept C129089157 @default.
- W4299321610 hasConcept C134306372 @default.
- W4299321610 hasConcept C184720557 @default.
- W4299321610 hasConcept C185592680 @default.
- W4299321610 hasConcept C198043062 @default.
- W4299321610 hasConcept C202444582 @default.
- W4299321610 hasConcept C22324862 @default.
- W4299321610 hasConcept C32834561 @default.
- W4299321610 hasConcept C33923547 @default.
- W4299321610 hasConcept C55112680 @default.
- W4299321610 hasConcept C55493867 @default.
- W4299321610 hasConcept C6183050 @default.
- W4299321610 hasConcept C6419321 @default.
- W4299321610 hasConcept C70710897 @default.
- W4299321610 hasConcept C81332173 @default.
- W4299321610 hasConcept C9376300 @default.
- W4299321610 hasConceptScore W4299321610C104317684 @default.
- W4299321610 hasConceptScore W4299321610C114614502 @default.
- W4299321610 hasConceptScore W4299321610C118615104 @default.
- W4299321610 hasConceptScore W4299321610C123222754 @default.
- W4299321610 hasConceptScore W4299321610C129089157 @default.
- W4299321610 hasConceptScore W4299321610C134306372 @default.
- W4299321610 hasConceptScore W4299321610C184720557 @default.
- W4299321610 hasConceptScore W4299321610C185592680 @default.
- W4299321610 hasConceptScore W4299321610C198043062 @default.
- W4299321610 hasConceptScore W4299321610C202444582 @default.
- W4299321610 hasConceptScore W4299321610C22324862 @default.
- W4299321610 hasConceptScore W4299321610C32834561 @default.
- W4299321610 hasConceptScore W4299321610C33923547 @default.
- W4299321610 hasConceptScore W4299321610C55112680 @default.
- W4299321610 hasConceptScore W4299321610C55493867 @default.
- W4299321610 hasConceptScore W4299321610C6183050 @default.
- W4299321610 hasConceptScore W4299321610C6419321 @default.
- W4299321610 hasConceptScore W4299321610C70710897 @default.
- W4299321610 hasConceptScore W4299321610C81332173 @default.
- W4299321610 hasConceptScore W4299321610C9376300 @default.
- W4299321610 hasLocation W42993216101 @default.
- W4299321610 hasOpenAccess W4299321610 @default.
- W4299321610 hasPrimaryLocation W42993216101 @default.
- W4299321610 hasRelatedWork W2063952793 @default.
- W4299321610 hasRelatedWork W2085374344 @default.
- W4299321610 hasRelatedWork W2385139564 @default.
- W4299321610 hasRelatedWork W2949399143 @default.
- W4299321610 hasRelatedWork W2969393242 @default.
- W4299321610 hasRelatedWork W3033404384 @default.
- W4299321610 hasRelatedWork W3049343291 @default.
- W4299321610 hasRelatedWork W3104660690 @default.
- W4299321610 hasRelatedWork W4287324999 @default.
- W4299321610 hasRelatedWork W78847291 @default.
- W4299321610 isParatext "false" @default.
- W4299321610 isRetracted "false" @default.
- W4299321610 workType "article" @default.