Countable additivity of Henstock-Dunford Integral and Orlicz Space

2019/09/29 by Hemanta Kalita, Bipan Hazarika, Kalita, Hemanta +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA

paper · pdf · doi:10.48550/arxiv.1910.00419

13 pages

openalex publication_date 2019/09/29 · arxiv created 2019/12/01 · arxiv updated 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a real Banach space X and probability space (Ω, Σ, μ) we characterize the countable additivity of Henstock-Dunford integral for Henstock integrable function taking values in X as those weakly measurable function g: Ω→ X for which \y^*g~: y^* ∈ B_X^* \ is relatively weakly compact in some separable Orlicz space L^ϕ(μ) . We find relatively weakly compact in some Orlicz space with Henstock-Gel'fand integral.

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