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On a metric of the space of idempotent probability measures

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On a metric of the space of idempotent probability measures

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Zaitov, AA. (2020). On a metric of the space of idempotent probability measures. Applied General Topology. 21(1):35-51. https://doi.org/10.4995/agt.2020.11865

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Título: On a metric of the space of idempotent probability measures
Autor: Zaitov, Adilbek Atakhanovich
Fecha difusión:
Resumen:
[EN] In this paper we introduce a metric on the space I(X) of idempotent probability measures on a given compact metric space (X; ρ), which extends the metric ρ. It is proven the introduced metric generates the pointwise ...[+]
Palabras clave: Compact metrizable space , Idempotent measure , Metrization
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2020.11865
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2020.11865
Tipo: Artículo

References

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M. Akian, Densities of idempotent measures and large deviations, Trans. Amer. Math. Soc. 351 (1999), 4515-4543. https://doi.org/10.1090/S0002-9947-99-02153-4

G. Choquet,Theory of capacities, Ann. Inst. Fourier 5 (1955), 131-295. https://doi.org/10.5802/aif.53

V. V. Fedorchuk, Triples of infinite iterates of metrizable functors, Math. USSR-Izv. 36, no. 2 (1991), 411-433. https://doi.org/10.1070/IM1991v036n02ABEH002028

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G. L. Litvinov, Maslov dequantization, idempotent and tropical mathematics: A brief introduction, Journal of Mathematical Sciences 140, no. 3 (2007), In this paper we introduce a metric on the space I(X) of idempotent probability measures on a given compact metric space (X; ρ), which extends the metric ρ. It is proven the introduced metric generates the pointwise convergence topology on I(X). 26-444. https://doi.org/10.1007/s10958-007-0450-5

G. L. Litvinov, V. P. Maslov and G. B. Shpiz, Idempotent (asymptotic) analysis and the representation theory, in: Asymptotic Combinatorics with Applications to Mathematical Physics, V. A. Malyshev and A. M. Vershik (eds.), Kluwer Academic Publ., Dordrecht (2002), 267-278. https://doi.org/10.1007/978-94-010-0575-3_13

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A. A. Zaitov, Geometrical and topological properties of a subspace $P_f(X)$ of probability measures, Russ Math. 63, no. 10 (2019), 24-32. https://doi.org/10.3103/S1066369X19100049

A. A. Zaitov and A. Ya. Ishmetov, Homotopy properties of the space $I_f(X)$ of idempotent probability measures, Math. Notes 106, no. 3-4 (2019), 562-571. https://doi.org/10.1134/S0001434619090244

A. A. Zaitov and Kh. F. Kholturaev, On interrelation of the functors P of probability measures and I of idempotent probability measures, Uzbek Mathematical Journal 4 (2014), 36-45.

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