Asymptotic Lₚ-convergence, which resembles convergence in Lₚ, was introduced in {alves2024mode}, motivated by a question in diffusive relaxation. The main purpose of this note is to compare asymptotic Lₚ-convergence with convergence in measure and in weak Lₚ spaces. One of the results obtained provides a characterization of convergence in measure on finite measure spaces in terms of asymptotic Lₚ-convergence.
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Alves et al. (2024) studied this question.
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