### $\mathcal{I}$-convergence and extremal $\mathcal{I}$-limit points

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L. Olivier proved in 1827 the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. We prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept.

Converging sequences in metric space have Hausdorff dimension zero, but their metric dimension (limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, respectively) can be positive. Dimensions of such sequences are calculated using a different approach for each type. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived....

In this paper we introduce a new sequence space $B{V}_{\sigma}(\mathcal{M},u,p,r,\parallel \xb7,...,\xb7\parallel )$ defined by a sequence of Orlicz functions $\mathcal{M}=\left({M}_{k}\right)$ and study some topological properties of this sequence space.