I know that there is a Fubini-Tonelli Theorem for complex measures, but, in the version that I have seen, both measures must have finite total variation. I would be interested in a generalization to signed measures where the variation is allowed to be infinite. For what I would like to prove the following restrictions would be acceptable: i) one of the measures can be a positive measure, in fact, the Lebesgue measure ii) the other measure is a signed measure that can take the value $+\infty$ but not $-\infty$. Is there a Fubini-Tonelli Theorem for this situation? References welcome.
2026-03-25 11:17:49.1774437469
Fubini-Tonelli for signed measures
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