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Resource-bounded measure has been deÿned on the classes E; E2; ESPACE; E2SPACE; REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under ÿnite variations and has outer measure ¡ 1 in C, then X has measure 0 in C. This result strengthens Lutz's resource-bounded generalization of the classical Kolmogorov zero-one law. It also gives a useful su cient condition for proving that a set has measure 0 in a complexity class.doi:10.1016/s0304-3975(02)00320-1 fatcat:tqsqew2wingjnd556zrshhnyw4