Exercise 2, § 2

Let G be a barreled space, H a semi-reflexive space, and F the space $\mathscr{L}_s(G; H)$. Let m be a vectorial measure on T, with values in F. Show that for every numerical function $f$ essentially integrable for m, $\int f\, dm \in F$. (Observe that F is semi-reflexive.) The case where $H = \mathbf{R}$.