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.

单词	Almost convergent sequence
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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