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Mar 17, 2014 at 21:36 comment added user42355 I was looking at different versions of Fubini's and Tonelli's theorems. For these one needs a basic understanding of product measures. This is just a simple question in that area. My conjecture is that $\mu$ is not always $\sigma$-subadditive, mainly because otherwise I would have seen this statement before. The smallest possible counterexample could occur when $|X_1| = |X_2| = 3$. However I think in that case $\mu$ is $\sigma$-subadditive, but this is not so easy to check.
Mar 17, 2014 at 20:27 comment added Nik Weaver I don't know whether it's easy until I try it. It kind of looks like homework, though. What is the context? (And what is ${\cal H}$?)
Mar 17, 2014 at 18:51 comment added user42355 No, it's not homework. Why, is it so easy?
Mar 17, 2014 at 18:27 comment added Nik Weaver Is this homework?
Mar 17, 2014 at 16:29 history asked user42355 CC BY-SA 3.0