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A Note on Well-Distributed Sequences

Published online by Cambridge University Press:  20 November 2018

B. H. Murdoch
B. H. Murdoch*
Affiliation:
Trinity College, Dublin
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A sequence is said to be well distributed (mod 1) (3, 4, 5) if the limit

(1.1)

exists, uniformly in p ≥ 0, for all intervals I in [0, 1], with length |I|, characteristic function where (x) is the fractional part of x. If (1.1) is true for p = 0 and all I in [0, 1] we say that is uniformly distributed (mod 1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 808 - 810
Copyright
Copyright © Canadian Mathematical Society 1965

References

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