Lemma A.1 is not correct?

[thanhnguyentang]

Hi Chen,

I check out the Lemma A.1 in the paper but the derivation at the $4^{th}$ equality sign ("=") seems not correct since you when you put $f(x,y)$ inside the integral $\int_{x'}$, you cannot change the index $x$ in $f(x,y)$ into the index $x'$ as in $f(x',y)$. Such a change does not lead to an equivalent expression. Would you mind checking it out?

Furthermore, the lemma claims it is true under suitable regularity conditions. So what is that suitable regularity conditions?

Thank Chen,

Bests,
-Thanh

If you are still interested, the is a nice response on stackoverflow : http://stats.stackexchange.com/questions/250838/integral-identity-of-lemma-contained-in-infogan-paper