text: Although GAN recently has attracted so many attentions,  the theory of GAN is very poor.  This paper tried to make a new insight of GAN from theories  and I think their approach is a good first step to build theories for GAN.  However, I believe this paper is not enough to be accepted.  The main reason is that the main theorem (Theorem 4.1) is too restrictive. 1.	There is no theoretical result for failed conditions.  2.	To obtain the theorem, they assume the optimal discriminator.  However, most of failed scenarios come from the discriminator dynamics as in Figure 2.  3.	The authors could make more interesting results using the current ingredients.  For instance, I would like to check the conditions on eta and T to guarantee d_TV(G_mu*, G_hat{mu})<= delta_1 when |mu*_1 – mu*_2| >= delta_2 and |hat{mu}_1 – hat{mu}_2| >= delta_3.  In Theorem 4.1, the authors use the same delta for delta_1, delta_2, delta_3.  So, it is not clear which initial condition or target performance makes the eta and T.