Generalizations of the Riesz convergence theorem for Lorentz spaces

Abstract

We generalize the classical Riesz convergence theorem to Lorentz spaces, i.e., if f, f1, f2, . . . ∈ L p,q such that fn → f (a.e. or in measure) and fn p,q → f p,q , then fn − f p,q → 0 as n → ∞.