Summary
Conditions are given on a nonnegative regular summability matrix A to ensure that for a given number α, 0 ≤ α ≤ 1, there exists a sequence x consisting of 0's and 1's such that Ax converges to α.
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Ćunjalo, F., Khan, M., Miller, H. et al. Summability matrices and sequences of 0's and 1's. Acta Math Hung 109, 147–155 (2005). https://doi.org/10.1007/s10474-005-0238-3
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DOI: https://doi.org/10.1007/s10474-005-0238-3