On asymptotically statistical equivalent sequences. (English) Zbl 1045.40003

Patterson, Richard F.

Demonstr. Math. 36, No. 1, 149-153 (2003).

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)].

MSC:

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

Citations:

Zbl 0447.40005