Pacific Journal of Mathematics

On the definition of normal numbers.

Ivan Niven and H. S. Zuckerman

Article information

Pacific J. Math., Volume 1, Number 1 (1951), 103-109.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 10.0X


Niven, Ivan; Zuckerman, H. S. On the definition of normal numbers. Pacific J. Math. 1 (1951), no. 1, 103--109.

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  • [1] Emile Borel, Les probabilitesdenombrables et leurs applicationsarithmetiques, Rend. Circ. Mat. Palermo 27 (1909), 247-271.
  • [2] D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc, 8 (1933), 254-260.
  • [3] J. F. Koksma, Diophantische Approximationen, Ergebnisse der Mathematik, Band 1, Heft 4, Springer, Berlin, 1937.
  • [4] Arthur H. Copeland and Paul Erdos, Note on normal numbers, Bull. Amer. Math. Soc, 52 (1946), 857-860.
  • [5] G. H. Hardy and E. M. Wright, The Theory of Numbers, Second Edition, Oxford University Press, London, 1945.