WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Factorizable convergence of random variables
in Grand Lebesgue Spaces
Authors: , ,
Abstract: 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 nonimprovable.
Keywords:
Probability, random variables, separable random process, convergence almost surely, Lebesgue-Riesz spaces, Grand Lebesgue Spaces, Young-Fenchel or Legendre transform, slowly varying
function, Bonferroni’s inequality, Tchebychev-Markov’s inequality, tail of distribution, Borel-Cantelli lemma
Pages: 389-397 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 24, 2025, Art. #37 DOI: 10.37394/23206.2025.24.37
