Construction of \(\mu \)-normal sequences (Q2634824)

The authors extend \textit{D. G. Champernowne}'s well-known construction of normal numbers [J. Lond. Math. Soc. 8, 254--260 (1933; Zbl 0007.33701)] to provide sequences which are generic for a given invariant probability measure. The construction works in a very general setting: for sequences over arbitrary finite alphabets and a given shift-invariant probability measure. This leads to normal numbers in standard \(q\)-ary expansions, in Lüroth series expansions, in \(\beta\)-expansions and with respect to continued fraction expansions.