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The Distribution of Sequences and Summability

Published online by Cambridge University Press:  20 November 2018

A. F. Dowidar  and
G. M. Petersen
A. F. Dowidar
Affiliation:
University College of Swansea
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We suppose that 0 < sn ≤ 1 for every n, and denote by n(α, β) the number of S0, S1, S2, . . . , Sn which fall in the interval 0 ≤ α < x ≤ β ≤ 1. If there exists a function g(t), 0 ≤ t ≤ 1, such that

for every interval (α, β] with 0 ≤ β — α ≤ 1, the sequence (Sn) is said to have a distribution function g(t), 0 ≤ t ≤ 1, in the interval [0, 1], (see 9, p. 87).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 1 - 10
Copyright
Copyright © Canadian Mathematical Society 1963

References

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