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JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2023 Volume 12(30), Issue 3, Pages 105–118 (Mi pa385)

The weak drop property and the de la Vallée Poussin Theorem

H. Kalita

Mathematics Division, VIT Bhopal University, Indore-Bhopal Highway, Sehore, Madhya Pradesh, India

Abstract: We prove that a closed bounded convex set is uniformly integrable if and only if it has the weak drop property. We extract the weakly compact subsets of the Henstock integrable functions on the H-Orlicz spaces with the weak drop property via de la Vallée Poussin Theorem.

Keywords: Young's function, weak drop property, H-Orlicz spaces.

UDC: 517.98

MSC: 46A55, 46B20

Received: 19.02.2023
Revised: 16.05.2023
Accepted: 28.05.2023

Language: English

DOI: 10.15393/j3.art.2023.13451



© Steklov Math. Inst. of RAS, 2024