We introduce balanced t(n)-genericity which is a refinement of the genericity concept of Ambos-Spies, Fleischhack and Huwig and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasticity. By uniformly describing these concepts and weaker notions of stochsticity introduced by Wilber and Ko in terms of prediction functions, we clarify the relations among these resource-bounded stochasticity concepts. Moreover, we give descriptions of these concepts in the framework of Lutz's resource-bounded measure theory based on martingales: We show that t(n)-stochasticity coincides with a weak notion of t(n)-randomness based on so-called simple martingales but that it is strictly weaker than t(n)-randomness in the sense of Lutz.
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