Abstract

The aim of this note is to present a new point of view for introducing all well-known modes of convergence of sequences of random variables. In the one hand, we start from two noteworthy sets in convergence viz $T_{j,\epsilon}$ and $S_{j,\epsilon}$. The consideration of certain progressive assumptions on both $T_{j,\epsilon}$ and $S_{j,\epsilon}$ gives rise to a part of convergence concepts going from uniform convergence to convergence in probability. On the other hand, some key inequalities implies the rest of convergence concepts whose link with the former scheme lies in uniform and in probability convergence which end the circle of convergence modes. Moreover, all these steps are illustrated with their respective methodological charts.

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