We study the classes of the form ALMOST-R, for R a reducibility. This includes, among others, the classes BPP, P, and PH. We give a characterization of this classes in terms of reductions to n-random languages, a subclass of algorithmically random languages. Also, we give a characterization of classes of the form ALMOST-R in terms of resource bounded measure, for R reductions of a restricted kind.
Book, R., Mayordomo, E. "On the robustness of ALMOST-R". 1993.