Abstract
Let $K$ be a convex lattice set in $\mathbb{Z}^n$ containing the origin as the interior of its convex hull. In this paper, the definition of the polar of a convex lattice set $K$ is given both in $\mathbb{Q}^n$ and $\mathbb{Z}^n$. Some properties and inequalities about the convex lattice sets and their polar are established.
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