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On asymptotically statistical equivalent sequences. (English) Zbl 1045.40003
Summary: This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent and statistically limit. Two nonnegative sequences \([x]\) and \([y]\) are said to be asymptotically statistical equivalents of multiple \(L\) provided that for every \(\varepsilon<0\), \(\lim_n\frac 1n\){the number of \(k\leq n:| \frac{x_k} {y_k}- L|\geq\varepsilon\}=0\) and simply asymptotically statistical equivalent if \(L=1\). In addition, there are also statistical analogs of theorems of I. P. Pobyvanents in [Mat. Fiz. 28, 83–87 (1980; Zbl 0447.40005)].

40A05 Convergence and divergence of series and sequences
42B15 Multipliers for harmonic analysis in several variables
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