   Perhaps counterintuitively, we begin with the case of infinite binary sequences. Which of these should count as random products of our binary process?  Each individual infinite sequence, whether orderly or not, has measure zero under the standard (Lebesgue) measure over the Cantor space. We cannot determine whether an individual sequence is random from considering what fraction it constitutes of the set of all such sequences. But, intuitively, almost all such infinite sequences should be random and disorderly, and only few will be orderly (an observation first due to Ville 1939). A typical infinite sequence is one without pattern; only exceptional cases have order to them. If the actual process that generate the sequences are perfectly deterministic, it may be that a typical product of that process is not random. But we are rather concerned to characterise which of all the possible sequences produced by any process whatsoever are random, and it seems clear that most of the ways an infinite sequence might be produced, and hence most of the sequences so produced, will be random. This fits with intuitive considerations: