  We must impose another condition to rule out the Champernowne sequence. We could proceed, piecemeal, in response to various problem cases, to successively introduce further stochastic properties, each of which is a necessary condition for randomness, eventually hoping to give a characterisation of the random sequences by aggregating enough of them together. Given the complex structure of the Cantor space, the prospects for success of such a cumulative approach seem dim. A more promising bolder route is to offer one stochastic property that is by itself necessary and sufficient for randomness, the possession of which will entail the possession of the other properties we’ve mentioned (the property of large numbers, Borel normality, etc.).