For a positive integer s(> 1), we say that the real number x is normal to base s or s-normal if the sequence (s n x) n-1 ∞ is uniformly distributed modulo one. Some 80 years ago Borel showed that almost all real numbers are normal to all bases. Some 40 years ago Steinhaus asked whether 2-normality coincides with 3-normality and Cassels answered the question in the negative (see ).
Unable to display preview. Download preview PDF.