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Re: [HM] question about term "normal"
Posted:
Oct 28, 2006 4:01 PM


Dear all Borelians, indeed, Borel is the one who coined the term and developed the concept of "normal" about the representation of the numbers in a given base. Here are some precisions and references.
Peter Flor: > in the book "Uniform dustribution of sequences" by KUIPERS and > NIEDERREITER. > According to these authors, the concept dates back to some publications > by Emile Borel, of 1909 and 1914.
1914 "most probably" refers to:  LE HASARD. Paris, Alcan 1914. Small in8
1909 is, of course the famous milestone paper:  Les probabilités dénombrables et leur applications arithmétiques, p. 247271 in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. T. 27 (1° semestre 1909), Palerme 1909. Great in8. where indeed, on p. 260, he defines "simplement normal" (in base 10) a fractional number when the frequency of its figures is 1/10. Then he goes on refining the concept, and defines "entièrement normal", and "absolument normal" numbers (this last refinement is on p. 261).
I find another important reference in 1926:  APPLICATIONS A L'ARITHMÉTIQUE ET A LA THÉORIE DES FONCTIONS Leçons professées à la Faculté des Sciences de Paris rédigées par Paul DUBREIL. Paris, GauthierVillars, 1926. Great in8. (Premier fascicule du Tome II du Traité du calcul des probabilités et de ses applications). where the first chapter goes back to the definitions quoted supra.
Udai Venedem http://aaaa.fr.eu.org/alta.mathematica/ 



