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Jan 14, 2021 at 14:56 comment added iolo Feel free to write an answer btw
Jan 14, 2021 at 14:44 comment added iolo I just encountered the same theorem in the paper. I am checking the details, but it seems to be correct :)
Jan 14, 2021 at 14:29 comment added Christian I think in your setting you only need that the integral $\int_V p(x)\,\mathrm{d}\nu(x)$ is finite for every $p\in\mathcal{P}$ - then the results in the above mentioned paper should give you that the integral is an element of $V$.
Jan 14, 2021 at 14:02 comment added Christian The following paper might be useful: G. Erik F. Thomas. Integration of functions with values in locally convex Suslin spaces. Trans. Amer. Math. Soc., 212:61–81, 1975
Jan 13, 2021 at 16:31 history asked iolo CC BY-SA 4.0