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Some Relations Between Various Types of Normality of Numbers

Published online by Cambridge University Press:  20 November 2018

H. A. Hanson
H. A. Hanson*
Affiliation:
Michigan State College
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In this paper certain relations will be proved between ∊-normality of integers, (k, ∊)-normality of integers, and normality of real numbers. Also a new type of normality of numbers will be introduced, namely, quasi-normality, as defined below.

A simply normal number is a real number, expressed in some scale B, in which each digit of the scale B occurs with the asymptotic frequency 1/B.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 477 - 485
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Besicovitch, A. S., The asymptotic distribution of the numerals in the squares of the natural numbers, Math. Z., 39 (1934), 146–156.Google Scholar
2. Borel, E., Les probabilités dénombrables et leur applications arithmétiques, Rend. Cire. Mat. Palermo, 27 (1909), 247–271.Google Scholar
3. de Bruijn, N. G., A combinatorial problem, Nederlandse Akad. Wetensch., Proc. 49, (1946), 758–764.Google Scholar
4. Cassels, J. W. S., On a paper of Niven and Zuckerman, Pacific J. Math., 2 (1952), 555–557.Google Scholar
5. Davenport, H. and Erdös, P., Note on normal numbers, Can. J. Math., 4 (1952), 58–63.Google Scholar
6. Goode, I. J., Normal recurring decimals, J. London Math. Soc, 21 (1946), 167–169.Google Scholar
7. Niven, I. and Zuckerman, H. S., On the definition of normal numbers, Pacific J. Math., 1 (1951), 103–109.Google Scholar
8. Rees, D., Note on a paper by I. J. Goode, J. London Math. Soc. 21, (1946), 169–172.Google Scholar
9. Wall, D. D., On normal numbers, Doctor's dissertation, University of California, 1949.Google Scholar