A stronger Kolmogorov zero-one law for resource-bounded measure

J.J. Dai
Proceedings 16th Annual IEEE Conference on Computational Complexity  
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:10.1109/ccc.2001.933887 dblp:conf/coco/Dai01 fatcat:7xw2ib3qgrbp7guvutl5eolylm