Resource-bounded measure on probabilistic classes

We extend Lutz's resource-bounded measure to probabilistic classes, and obtain notions of resource-bounded measure on probabilistic complexity classes such as BPE and BPEXP . Unlike former attempts, our resource bounded measure notions satisfy all three basic measure properties, that is every singleton { L } has measure zero, the whole space has measure one, and “enumerable infinite unions” of measure zero sets have measure zero.