  While the above approach, with the modifications suggestion in the supplement taken on board, does permit biased random sequences, it comes at a cost. While the Lebesgue measure is a natural one that is definable on the Cantor space of sequences directly, the generalisation of ML-randomness requires an independent computable probability measure on the space of sequences to be provided. While this may be done in cases where we antecedently know the chances, it is of no use in circumstances where the existence of chance is to be inferred from the existence of a random sequence of outcomes, in line with RCT—for every sequence there is some chance measure according to which it is random, which threatens to trivialise the inference from randomness to chance. As Earman (1986: 145) also emphasises, this approach to randomness seems to require essentially that the chanciness of the process producing the random sequence is conceptually prior to the sequence being random. This kind of process approach to randomness has some intuitive support, and we will return to it below (§6.2), but it risks turning RCT into an uninformative triviality. By contrast, the Lebesgue measure has the advantage of being intrinsically definable from the symmetries of the Cantor space, a feature other computable measures lack.