In this paper we prove that the classical Brunn–Minkowski inequality holds for product measures on the Euclidean space with quasi-convex densities when considering certain classes of sets that contain, among others, the complements (within a centered box) of unconditional sets. As a consequence, we derive an isoperimetric type inequality.

中文翻译：

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关于具有准凸密度的度量的Brunn-Minkowski不等式

在本文中，我们证明了经典的Brunn–Minkowski不等式在考虑包含非条件集的补集（在中心框内）的某些类集时，具有拟凸密度的欧氏空间上的乘积度量成立。结果，我们得出了等距类型的不等式。