Factorizable convergence of random variables in Grand Lebesgue Spaces

Maria Rosaria Formica; Eugeny Ostrovsky; Leonid Sirota

doi:10.37394/23206.2025.24.37

Factorizable convergence of random variables in Grand Lebesgue Spaces

Maria Rosaria Formica
, Eugeny Ostrovsky
, Leonid Sirota

Department of Mathematics

University of Naples Parthenope

Research output: Contribution to journal › Article › peer-review

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 non-improvable.

Original language	English
Pages (from-to)	389-397
Number of pages	9
Journal	WSEAS Transactions on Mathematics
Volume	24
DOIs	https://doi.org/10.37394/23206.2025.24.37
State	Published - 2025

Bibliographical note

Publisher Copyright:
© 2025 World Scientific and Engineering Academy and Society. All rights reserved.

Keywords

Bonferroni’s inequality
Borel-Cantelli lemma
Grand Lebesgue Spaces
Lebesgue-Riesz spaces
Probability
Tchebychev-Markov’s inequality
Young-Fenchel or Legendre transform
convergence almost surely
random variables
separable random process
slowly varying function
tail of distribution

UN SDGs

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10.37394/23206.2025.24.37

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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 non-improvable.",

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AU - Formica, Maria Rosaria

AU - Ostrovsky, Eugeny

AU - Sirota, Leonid

PY - 2025

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N2 - 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.

AB - 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.

KW - Bonferroni’s inequality

KW - Borel-Cantelli lemma

KW - Grand Lebesgue Spaces

KW - Lebesgue-Riesz spaces

KW - Probability

KW - Tchebychev-Markov’s inequality

KW - Young-Fenchel or Legendre transform

KW - convergence almost surely

KW - random variables

KW - separable random process

KW - slowly varying function

KW - tail of distribution

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AN - SCOPUS:105009258957

SN - 1109-2769

VL - 24

SP - 389

EP - 397

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

ER -

Factorizable convergence of random variables in Grand Lebesgue Spaces

Abstract

Bibliographical note

Keywords

UN SDGs

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