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A Generalized Tauberian Theorem
Published online by Cambridge University Press: 20 November 2018
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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.
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- Research Article
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- 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
3. Keogh, F. R. and Petersen, G. M., A universal Tauberian theorem, J. Lond. Math. Soc. (to appear).Google Scholar
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