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Hille's theorem is a powerful classical result in vector measure theory. Itasserts that the application of a closed, unbounded linear operator commuteswith strong/Bochner integration of functions taking values in a Banach space.This note shows that Hille's theorem also holds in the setting of completelocally convex spaces.

Hille's theorem for Bochner integrals of functions with values in locally convex spaces