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About: Almost convergent sequence     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatSequencesAndSeriesyago:Abstraction100002137yago:Arrangement107938773yago:Group100031264yago:Ordering108456993yago:Sequence108459252yago:Series108457976 New Facet based on Instances of this Class

A bounded real sequence is said to be almost convergent to if each Banach limit assignsthe same value to the sequence . Lorentz proved that is almost convergent if and only if uniformly in . The above limit can be rewritten in detail as Almost convergence is studied in summability theory. It is an example of a summability methodwhich cannot be represented as a matrix method.