2021-09-23T00:27:14Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000402122021-03-01T21:05:24ZOn a Certain Metric on the Space of Pairs of a Random Variable and a Probability MeasureKusuoka, Shigeo138807Nakayama, Toshiyuki138808415certain metricrandom variableprobability measureapplication/pdfThe authors introduce new metrics on the space of pairs of a random variable and a probability measure over a Polish space, and study the properties of them. Finally, as an application, they discuss how the integrand for the martingale representation converges in the invariance principle.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2001application/pdfJournal of mathematical sciences, the University of Tokyo28343356AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40212/files/jms080209.pdfeng