Abstract
In 1900 Pringsheim presented the following definition for convergence of a double sequence (i.e. ordinary infinite matrices). A double sequence [x] has limit L if the terms of the double sequence approaches L as both the column and row indices increases. Using this notion for convergence I will present definitions for asymptotically equivalent double sequences, rate preserving four dimensional matrix transformation, and these definitions shall be used to present two natural invariance theorems.
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AMS Subject Classification (2000): Primary 42B15, Secondary 40C05
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Patterson, R.F. Rates of Convergence for Double Sequences. SEA bull. math. 26, 469–478 (2003). https://doi.org/10.1007/s10012-002-0469-y
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DOI: https://doi.org/10.1007/s10012-002-0469-y