<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We study measurable real valued multipliers of variationally McShane (resp. McShane) integrable functions defined on a <italic>σ</italic>-finite outer regular quasi-Radon measure space and taking values in a complete locally convex topological vector space <italic>X</italic>. We also show: in case <italic>X</italic> 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 <italic>X</italic> is representable by semi-norm.</p>
</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.

Multipliers of Variationally Mcshane Integrable Functions in Locally Convex Space

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

We study measurable real valued multipliers of variationally McShane (resp. McShane) integrable functions defined on a σ-finite outer regular quasi-Radon...

Multipliers of Variationally Mcshane Integrable Functions in Locally Convex Space

Published Online: Nov 16, 2023

Page range: 17 - 26

Received: Aug 20, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0021

Keywords
variationally McShane integrable, integrable by semi-norm, Pettis integrable, Fréchet space, quasi-Radon measure space

© 2023 Savita Bhatnagar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Multipliers of Variationally Mcshane Integrable Functions in Locally Convex Space

Published Online: Nov 16, 2023

Page range: 17 - 26

Received: Aug 20, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0021

Keywordsvariationally McShane integrable, integrable by semi-norm, Pettis integrable, Fréchet space, quasi-Radon measure space

© 2023 Savita Bhatnagar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
variationally McShane integrable, integrable by semi-norm, Pettis integrable, Fréchet space, quasi-Radon measure space