Slowness---a measure of convergence of sequences (Q2774520)

A real-valued parameter called (upper, lower) slowness is assigned to every sequence of real numbers converging to zero, aiming to measure how slow the convergence is. The definition of slowness was motivated by the notion of metric dimension, known also as box counting dimension, or entropy dimension. The authors provide examples of calculation of slowness, and show that its value can decide the summability of the sequence. The decisive strength of such summability test is compared to logarithmic and Raabe's tests. Finally, it is shown that for any summable sequence, its upper slowness is equal to the upper metric dimension of the set of its partial sums.