2021-11-30T23:53:31Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/691132018-04-25T23:44:06Zhdl_2115_45007hdl_2115_116Equivalent conditions on the centrallimit theorem for a sequence of probability measures on RMikami, T.410In this paper we give equivalent conditions on the central limit theorem in total variation norm for a sequence of probability measures on R. This generalizes Cacoullos, Papathanasiou and Utev's central limit theorem in L1-norm for a sequence of probability density functions on R. We also give equivalent conditions on the central limit theorem in weak convergence and those on the local limit theorem.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69113info:doi/10.14943/83509https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69113/1/pre363.pdfHokkaido University Preprint Series in Mathematics363171996-12-01engpublisher