I am looking for a reference where the Fubini theorem for Radon measures is proved but so far I have not found anything.
What I have seen so far is that if we have a Radon measure $\mu$ on $X$ and $\nu$ on $Y$ then we are able to build a radon measure on $X \times Y$ using the Riez representation theorem and the fact that $X$ and $Y$ are locally compact and Hausdorff.
However when it comes to the Fubini theorem I have only seen it proved for the case where $X$ and $Y$ are $\sigma$-finite, and I would wish to prove it in a case where $X$ and $Y$ are not $\sigma$-finite. Is this possible? I have seen a book state that this fact is true.