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In this paper, we reduce pointwise convergence of polynomial ergodic averagesof general measure-preserving system acted by $\mathbb{Z}^{d}$ to the case ofmeasure-preserving system acted by $\mathbb{Z}^{d}$ with zero entropy. As anapplication, we can build pointwise convergence of polynomial ergodic averagesfor $K$-system acted by $\mathbb{Z}^{d}$.

Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$