We characterize the closed convex subsets of $${\mathbb {R}}^{n}$$ which have open or closed Gauss ranges. Some special attention is paid to epigraphs of lower semicontinuous convex functions.

中文翻译：

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具有开或闭高斯范围的闭凸集

我们刻画了 $${\mathbb {R}}^{n}$$ 的闭凸子集，它们具有开或闭的高斯范围。特别注意下半连续凸函数的题词。