ANALOGUES OF SOME FUNDAMENTAL THEOREMS OF SUMMABILITY THEORY

By Richard F. Patterson. 2000

86 citations recorded by the source corpus.

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0's and 1's which is not A-summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x. In this paper, defini- tions for "subsequences of a double sequence" and "Pringsheim limit points" of a double sequence are introduced. In addition, multidimensional analogues of Steinhaus' and Buck's theorems are proved.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0ae811f73c3e4c8cf0c26038dcd2d460aedc5696

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In Statistics and Probability

1. Ekrem Savas
2. Richard F. Patterson

Citations in the corpus

• Lacunary statistical convergence of double sequences (2005, background): “The following notion of a subsequence which was presented by Patterson in [9] will help us achieve our objectives: Definition 1.”