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It is shown that under suitable regularity conditions, differential entropyis a Lipschitz functional on the space of distributions on $n$-dimensionalEuclidean space with respect to the quadratic Wasserstein distance. Undersimilar conditions, (discrete) Shannon entropy is shown to be Lipschitzcontinuous in distributions over the product space with respect to Ornstein's$\bar d$-distance (Wasserstein distance corresponding to the Hamming distance).These results together with Talagrand's and Marton's transportation-informationinequalities allow one to replace the unknown multi-user interference with itsi.i.d. approximations. As an application, a new outer bound for the two-userGaussian interference channel is proved, which, in particular, settles the"missing corner point" problem of Costa (1985).

Wasserstein continuity of entropy and outer bounds for interference channels