Abstract
Hausdorff methods have been extensively investigated by F. Hausdorif and others [1, 3, 5].1 A of summation A is said to be stronger than another B if every sequence summed by B is also summed by A. Two methods of summation are consistent if any sequence which can be summed by both methods has the same limit assigned to it by both of them. I shall say that A contains B if A is stronger than B and also consistent with B. A containing ordinary convergence is called regular. F. Hausdorff proved that any two regular Hausdorff methods are consistent [3]. This enabled R. P. Agnew to introduce the collective Hausdorff method I by the definition: { Sn } is summable & to the sum S if { Sn } is summable to S by any regular Hausdorff [1]. He raised at the same time the question whether there is a matrix of summation containing ,. I shall now show that the answer is in the negative. More precisely I prove the following:
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