Hille's Theorem for Bochner Integrals of Functions with Values in Locally Convex Spaces

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.