论文标题
锥理论的barycenter定理
A cone-theoretic barycenter existence theorem
论文作者
论文摘要
我们表明，本地凸出，凸出，清醒的拓扑锥体$ \ mathfrak {c} $上的每个连续估值都有一个Barycenter。这个barycenter是独一无二的，barycenter映射$β$是连续的，因此，是$ \ Mathbf v _ {\ Mathrm W} $ - Algebra的结构图，即Eilenberg-Moore代数，是$ T_0 $ t_0 $ topolotic space ot Todalde $ topolotic space of to eilenberg-moore代数。实际上，它是唯一的$ \ mathbf v _ {\ mathrm w} $ - 代数，它诱导了$ \ mathfrak {c} $上的圆锥结构。
We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone $\mathfrak{C}$ has a barycenter. This barycenter is unique, and the barycenter map $β$ is continuous, hence is the structure map of a $\mathbf V_{\mathrm w}$-algebra, i.e., an Eilenberg-Moore algebra of the extended valuation monad on the category of $T_0$ topological spaces; it is, in fact, the unique $\mathbf V_{\mathrm w}$-algebra that induces the cone structure on $\mathfrak{C}$.
