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Jul 11, 2017 at 17:03 comment added paul garrett @LSpice, of course you're right, for the t.d. case no assumption is needed. I reflexively say "quasi-complete (locally convex)" because of the archimedean case. :)
Jul 11, 2017 at 16:32 comment added LSpice Do you really need any assumptions on $V$? A compactly supported, locally constant function is a combination of constant multiples of characteristic functions, i.e., lies in $\mathrm C_{\mathrm c}^\infty \otimes_{\mathbb C} V$, and for such functions integration is easy.
Jul 10, 2017 at 20:41 comment added darkl I don't really need the compact support, Thank you!
Jul 10, 2017 at 20:41 vote accept darkl
Jul 10, 2017 at 20:27 history answered paul garrett CC BY-SA 3.0