| Автор | Thorpe, B. |
| Дата выпуска | 1980 |
| dc.description | 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). |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Edinburgh Mathematical Society 1980 |
| Название | A Cauchy criterion for the summability of an infinite integral |
| Тип | research-article |
| DOI | 10.1017/S0013091500003096 |
| Electronic ISSN | 1464-3839 |
| Print ISSN | 0013-0915 |
| Журнал | Proceedings of the Edinburgh Mathematical Society |
| Том | 23 |
| Первая страница | 219 |
| Последняя страница | 224 |
| Аффилиация | Thorpe B.; The University |
| Выпуск | 2 |
