This article discusses relations between several notions of continuity in rank-dependent utility, and in the generalized version of rank-dependent utility as initiated by Segal. Primarily, examples are given to show logical independencies between these notions of continuity. This also leads to counterexamples to Segal's (1989) characterizing theorem 1. This article is a rewritten version of Wakker (1990a). Puppe (1990) independently discovered that Segal's (1989) theorem 1 is not correct. This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.

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Keywords qualitative probability, rank-dependent utility
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Wakker, P.P.. (1993). Counterexamples to Segal's measure representation theorem. Journal of Risk and Uncertainty, 6(1), 91–98. doi:10.1007/BF01065352