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A Generalized Tauberian Theorem

Published online by Cambridge University Press:  20 November 2018

F. R. Keogh  and
G. M. Petersen
F. R. Keogh
Affiliation:
University College of Swansea
G. M. Petersen
Affiliation:
University College of Swansea
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Extract

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Let {s(n)} be a real sequence and let x be any number in the interval 0 < x ⩽ 1. Representing x by a non-terminating binary decimal expansion we shall denote by {s(n,x)} the subsequence of {s(n)} obtained by omitting s(k) if and only if there is a 0 in the decimal place in the expansion of x. With this correspondence it is then possible to speak of “a set of subsequences of the first category,” “an everywhere dense set of subsequences,” and so on.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 111 - 114
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Bowen, N. A. and Macintyre, A. J., An oscillation theorem of Tauberian type, Quart. J. Math., 2 (1950), 243-247.Google Scholar
2. Buck, R. C., A note on subsequences Bull. Amer. Math. Soc, 49 (1943), 898-899.Google Scholar
3. Keogh, F. R. and Petersen, G. M., A universal Tauberian theorem, J. Lond. Math. Soc. (to appear).Google Scholar