Criterion for convergence almost everywhere, with applications

Abstract

We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.

References in corpus (1)

• A multiparameter Garsia-Rodemich-Rumsey inequality and some applications

Cited by in corpus (4)

• Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Cramer's condition
• Entropy and Grand Lebesgue Spaces approach for Prokhorov-Skorokhod continuity of random processes, with tail estimates
• Prokhorov-Skorokhod continuity of random fields. A natural approach
• Fourier transform acting on the functions defined in the infinite LCA groups. A Grand Lebesgue Spaces approach