Abstract
If a ∈ L(1, T) for every finite T>1, then we say that the infinite integral a(u)du is convergent with sum s if a(u)du = s. It is well known that a necessary and sufficient condition for a(u)du to be convergent (with some finite sum s) is that Cauchy's criterion,holds. The object of this note is to obtain a similar result for summability (C, α) of a(u) du which reduces to Cauchy's criterion in the case of convergence. The corresti ponding problem for summable series has been treated by A. F. Andersen in (1).
Publisher
Cambridge University Press (CUP)
Reference6 articles.
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