This article is cited in 2 papers

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