  Recalling the definition of effective measure zero from  supplement  B.2,  Martin-Löf suggests that a random sequence is any that does not belong to any effective measure zero set of sequences, and thus belongs to every effective measure one set of sequences. An effective measure zero set of sequences will contain sequences which can be effectively determined to have a ‘special hallmark’ (for example, having a ‘1’ at every seventh place, or never having the string ‘000000’ occurring as a subsequence). It is part of von Mises’ insight that no random sequence will possess any of these effectively determinable special hallmarks: such hallmarks would permit exploitation as part of a gambling system. But Martin-Löf notices that all of the commonly used measure one properties of stochasticity are effective measure one. Any sequence which violates the property of large numbers, or the law of symmetric oscillations, etc., will do so on increasingly long initial subsequences. So the violation of any such property will also be a special hallmark of a non-random sequence, an indicator that the sequence which possesses it is an unusual one. Since the unusual properties of non-stochasticity in question are effective measure zero, we can therefore say that the random sequences are those which are not special in any effectively determinable way. To formalise this, Martin-Löf appeals to the language of significance testing. His main result is sometimes put as the claim that random sequences as those which pass all recursive significance tests for sequences (Schnorr 1971: §1)—they are never atypical enough to prompt us to reject the hypothesis that they are random. See supplement  B.1.1  for more detail on this point.