On the history of martingales in the study of randomness.
Coherent randomness tests and computing the -trivial sets
We introduce Oberwolfach randomness, a notion within Demuth’s framework of statistical tests with moving components; here the components’ movement has to be coherent across levels. We show that a ML-random set computes all -trivial sets if and only if it is not Oberwolfach random, and indeed that there is a -trivial set which is not computable from any Oberwolfach random set. We show that Oberwolfach random sets satisfy effective versions of almost-everywhere theorems of analysis, such as the...
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