In this note, we provide a simple proof of some properties enjoyed by convex functions having the engulfing property. In particular, making use only of results peculiar to convex analysis, we prove that differentiability and strict convexity are conditions intrinsic to the engulfing property.

中文翻译：

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从凸分析的角度看吞没性质

在本笔记中，我们提供了具有吞没性质的凸函数所享有的一些性质的简单证明。特别是，仅利用凸分析特有的结果，我们证明了可微性和严格凸性是吞噬性质的内在条件。