  One such further property is Borel normality, also defined in that paper by Borel. A sequence is Borel normal iff each finite string of digits of equal length has equal frequency in the  sequence.[6]  Borel proved that a measure one set of sequences in the Cantor space are Borel normal. Borel normality is a useful condition to impose for random sequences, as it has the consequence that there will be no predictable pattern to the sequence: for any string \(\sigma\) appearing multiple times in a sequence, it will as commonly be followed by a 1 as by a 0. This lack of predictability based on the previous elements of the sequence is necessary for genuine randomness. But again Borel normality is not sufficient for randomness. The Champernowne sequence (Champernowne 1933) is the sequence of digits in the binary representations of each successive non-negative integer: