No van Dam–Veltman–Zakharov discontinuity in AdS space

We prove that the van Dam–Veltman–Zakharov discontinuity arising in the massless limit of massive gravity theories is peculiar to Minkowski space and it is not present in anti-de Sitter space, where the massless limit is smooth. More generally, the massless limit is smooth whenever the square of the graviton mass vanishes faster than the cosmological constant.