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A probabilistic metric space is a generalization of metric spaces where the distance is no longer valued in non-negative real numbers, but instead is valued in distribution functions. Let ''D''+ be the set of all probability distribution functions ''F'' such that ''F''(0) = 0: ''F'' is a nondecreasing, right continuous mapping from the real numbers R into (1 ) such that :sup ''F''(''x'') = 1 where the supremum is taken over all ''x'' in R. The ordered pair (''S'',''d'') is said to be a probabilistic metric space if ''S'' is a nonempty set and :''d'': ''S''×''S'' →''D''+ In the following, ''d''(''p'', ''q'') is denoted by ''d''''p'',''q'' for every (''p'', ''q'') ∈ ''S'' × ''S'' and is a distribution function ''d''''p'',''q''(x). The distance-distribution function satisfies the following conditions: *''d''''u'',''v''(''x'') = 1 for all ''x'' > 0 ⇔ ''u'' = ''v'' (''u'', ''v'' ∈ ''S''). *''d''''u'',''v''(''x'') = ''d''''v'',''u''(''x'') for all ''x'' and for every ''u'', ''v'' ∈ ''S''. *''d''''u'',''v''(''x'') = 1 and ''d''''v'',''w''(''y'') = 1 ⇒ ''d''''u'',''w''(''x'' + ''y'') = 1 for ''u'', ''v'', ''w'' ∈ S and ''x'', ''y'' ∈ R. == See also == * Statistical distance 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「probabilistic metric space」の詳細全文を読む スポンサード リンク
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