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In this paper, two notes about the ergodicity of partially hyperbolic systems are given. First one is the ergodicity for a C2 volume preserving partially hyperbolic diffeomorphism of a smooth compact Riemannian manifold which is essentially accessible and weak central exponentially bunched. Second one is that for a C2 partially hyperbolic diffeomorphism, if both forward and backward center bunched are a full probability set, then it is center bunched in the sense of [Burns & Wilkinson, 2010].