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We present a notion of resource-bounded m e asure for P and other subexponential-time classes. This generalization is based on Lutz's notion of measure, but overcomes the limitations that cause Lutz's de nitions to apply only to classes at least as large as E. W e p r esent many of the basic properties of this measure, and use it to explore the class of sets that are hard for BPP. Bennett and Gill showed that almost all sets are hard for BPP; Lutz improved this from Lebesgue measure t o m edoi:10.1109/sfcs.1994.365713 dblp:conf/focs/AllenderS94 fatcat:s52duvyslbf4rnbcxqsxsank4m