Multipliers of Variationally Mcshane Integrable Functions in Locally Convex Space

Bhatnagar, Savita

doi:10.2478/tmmp-2023-0021

Abstract

We study measurable real valued multipliers of variationally McShane (resp. McShane) integrable functions defined on a σ-finite outer regular quasi-Radon measure space and taking values in a complete locally convex topological vector space X. We also show: in case X is representable by semi-norm then essentially bounded real measurable functions are multipliers of functions which are Pettis integrable as well as integrable by semi-norm. The space of real valued measurable and essentially bounded functions turn out to be precisely the multipliers of variationally McShane (resp. McShane) integrable functions in case X is representable by semi-norm.

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Multipliers of Variationally Mcshane Integrable Functions in Locally Convex Space

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