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Densities and Measures of Linear Sets

Published online by Cambridge University Press:  20 November 2018

B. G. A. Kelly
B. G. A. Kelly*
Affiliation:
University of Toronto, Toronto, Ontario
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If In, I∞ denote the intervals [0, n), [0, ∞) respectively, we propose to examine the properties of an upper and lower density

(1)

(1)

of a set S belonging to the power set of I∞ where m*,m* denote the outer and inner (linear) Lebesgue measures.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 61 - 66
Copyright
Copyright © Canadian Mathematical Society 1973

References

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3. Knopp, K., Mengentheoretische Behandlung einiger Problème der diophantischen Approximationen und der transfiniten Wahrscheinlichkeiten, Math. Ann. 95 (1926), 409–426.Google Scholar
4. Niven, I., Uniform distribution of sequences of integers, Trans. Amer. Math. Soc. 98 (1961), 52–61.Google Scholar