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I am still not fully through this topic, but some entry publications are the following:
Menger, Karl, and Karl Menger. "Statistical metrics." Selecta Mathematica: Volume 2 (2003): 433-435.
Kramosil, Ivan, and Jiří Michálek. "Fuzzy metrics and statistical metric spaces." Kybernetika 11.5 (1975): 336-344.
Schweizer, Berthold, and Abe Sklar. "Statistical metric spaces." Pacific J. Math 10.1 (1960): 313-334.
Especially the definition of a metric in the probability metric space is missing in the article. Looking at the article of t-norm could help to fill this page. 2003:E3:740:1000:20AB:8B31:5321:2830 (talk) 14:40, 18 October 2023 (UTC)[reply]