Factorizable convergence of random variables in Grand Lebesgue Spaces

We obtain results concerning the so-called factorization for the convergence almost everywhere of random variables belonging to the classical Lebesgue-Riesz spaces and we extend these results to the Grand Lebesgue Spaces. We also give exact estimates for the parameters involved and we provide several examples. Moreover, we show that in the general case the obtained estimates are, up to a multiplicative constant, essentially non-improvable.