Equidistribution for non-pluripolar currents on compact K\"ahler manifolds

Let $X$ be a compact K\"ahler manifold of complex dimension $k\ge 2$ and $f:X\to X$ a surjective holomorphic endomorphism of simple action on cohomology. We prove that the sequence of normalized pull-backs of a non-pluripolar current under iterates of $f$ converges to the Green current associated with $f$.