  Generative Adversarial Networks have become a core technique in Machine
Learning to generate unknown distributions from data samples. They have been
used in a wide range of context without paying much attention to the possible
theoretical limitations of those models. Indeed, because of the universal
approximation properties of Neural Networks, it is a general assumption that
GANs can generate any probability distribution. Recently, people began to
question this assumption and this article is in line with this thinking. We
provide a new result based on Extreme Value Theory showing that GANs can't
generate heavy tailed distributions. The full proof of this result is given.
