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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 oncohomology. We prove that the sequence of normalized pull-backs of anon-pluripolar current under iterates of $f$ converges to the Green currentassociated with $f$.

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