In this paper we deal with the problem of proving some versions of limit theorems when the pointwise convergence of the measures involved is replaced by the weaker ideal pointwise convergence. In the general case, the answer is negative, as it is shown by means of an example. However, it is possible to do some answers, in particular cases. In this paper, as examples of limit theorems, we prove some Schur-type and basic matrix theorems with respect to ideal convergence.
Schur and matrix theorems with respect to I-convergence
BOCCUTO, Antonio;
2011
Abstract
In this paper we deal with the problem of proving some versions of limit theorems when the pointwise convergence of the measures involved is replaced by the weaker ideal pointwise convergence. In the general case, the answer is negative, as it is shown by means of an example. However, it is possible to do some answers, in particular cases. In this paper, as examples of limit theorems, we prove some Schur-type and basic matrix theorems with respect to ideal convergence.File in questo prodotto:
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