Published April 1968
| public
Journal Article
Countable and net convergence
- Creators
- Marsden, J. E.
Abstract
It is well known that Lebesgue's dominated convergence theorem does not hold for nets; that is, having a countable sequence is essential. On the other hand, for a real valued function on an interval, sequences do suffice; that is, lim_(x → y)f(x) = a iff lim_(n → ∞)f(x_n) = a for every sequence x_n → y. The purpose of this note is to isolate the basic reasons for these phenomena.
Additional Information
© 1968. Reprinted from the American Mathematical Monthly.Additional details
- Eprint ID
- 19628
- Resolver ID
- CaltechAUTHORS:20100824-104216924
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2010-09-09Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field