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词汇 Almost convergent sequence
分类 英语词汇 英语翻译词典
释义

Almost convergent sequence

英语百科

Almost convergent sequence

A bounded real sequence (x_n) is said to be almost convergent to L if each Banach limit assigns the same value L to the sequence (x_n).

Lorentz proved that (x_n) is almost convergent if and only if

uniformly in n.

The above limit can be rewritten in detail as

Almost convergence is studied in summability theory. It is an example of a summability method which cannot be represented as a matrix method.

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