Abstract
Hille's theorem is a powerful classical result in vector measure theory. It asserts that the application of a closed, unbounded linear operator commutes with strong/Bochner integration of functions taking values in a Banach space. This note shows that Hille's theorem also holds in the setting of complete locally convex spaces.
Funding Statement
For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Citation
T. J. Sullivan. "Hille's Theorem for Bochner Integrals of Functions with Values in Locally Convex Spaces." Real Anal. Exchange 49 (2) 377 - 388, 1 October 2024. https://doi.org/10.14321/realanalexch.49.2.1719547551
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