Almost convergent sequence  A bounded real sequence formula_1 is said to be "almost convergent" to formula_2 if each Banach limit assigns the same value formula_2 to the sequence formula_1. Lorentz proved that formula_1 is almost convergent if and only if uniformly in formula_7. 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.