Fuzzy ultrametrics on the setofprobability measures
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2009
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Abstract
Weintroduceafuzzyultrametriconthesetofprobabilitymeasureswithcompactsupport defined on a fuzzy metric space. The construction is a counterpart, in the realm of fuzzy ultrametricspaces,oftheconstructionduetoVinkandRuttenofanultrametricontheset ofprobabilitymeasureswithcompactsupportsonanultrametricspace. It is proved that the set of probability measures with finite supports is dense in the naturaltopologygeneratedbythedefinedfuzzyultrametric.
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Savchenko, A. Fuzzy ultrametrics on the set of probability measures / A. Savchenko, M. Zarichnyi // Topology. – 2009. – V. 48, № 2-4. – Р. 130-136.