Affine dual Minkowski problem for general measures

Abstract: In 2025, the affine dual curvature measures $\widetilde{C}_m<sup>a(K,\cdot)$ of convex body $K$ were introduced by Cai, Leng, Wu, and Xi, and the even Minkowski problem for the affine dual curvature measures was solved. In this paper, the necessary and sufficient condition of affine dual Minkowski problem for general measures with $m&gt;1$ are proposed.