Explicit construction of normal lattice configurations

Volume 102 / 2005

Mordechay B. Levin, Meir Smorodinsky Colloquium Mathematicum 102 (2005), 33-47 MSC: Primary 11K16, 28D. DOI: 10.4064/cm102-1-4


We extend Champernowne's construction of normal numbers to base $b$ to the ${\mathbb Z}^d$ case and obtain an explicit construction of a generic point of the ${\mathbb Z}^d$ shift transformation of the set $\{ 0,1,\ldots,b-1 \}^{{\mathbb Z}^d}$.


  • Mordechay B. LevinDepartment of Mathematics and Statistics
    Bar-Ilan University
    52900 Ramat-Gan, Israel
  • Meir SmorodinskySchool of Mathematical Sciences
    Tel Aviv University
    Tel Aviv 69978, Israel

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