We study dually epi-translation invariant valuations on cones of convex functions containing the space of finite-valued convex functions. The existence of a homogeneous decomposition is used to associate a distribution to every valuation of this type similar to the Goodey-Weil embedding for translation invariant valuations on convex bodies. The relation between the valuation and its associated distribution is used to establish a notion of support for valuations. As an application, we show that there are no $\mathrm{SL}(n)$ or translation invariant valuations except constant valuations in this class and we discuss which valuations on finite-valued convex functions can be extended to larger cones. In addition, we examine some topological properties of spaces of valuations with compact support.

我们研究包含有限值凸函数空间的凸函数锥上的双重Epi-平移不变估值。均质分解的存在用于将分布与该类型的每个估值相关联，类似于凸体上平移不变估值的Goodey-Weil嵌入。评估及其关联分布之间的关系用于建立对评估的支持的概念。作为一个应用程序，我们表明没有$\mathrm{SL}（ñ）$或平价不变估值，但此类中的不变估值，我们讨论了有限值凸函数上的哪些估值可以扩展到更大的圆锥。此外，我们在紧密支持下研究了估值空间的某些拓扑性质。