Codensity and the Giry monad
Codensity and the Giry monad
复制标题
代码密度和吉里单子
DOI：
10.1016/j.jpaa.2015.08.017
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发表时间：
2014
影响因子：
0.8
通讯作者：
T. Avery
中科院分区：
文献类型：
--
作者：
T. Avery
在可测空间范畴上的吉里单子将一个空间发送到其上的所有概率测度的空间。还有一种有限可加性矩阵，其中概率测度用有限可加性测度代替。我们给出了有限和可数加性概率测度在积分算子上的表征，给出了对吉丽单元的一种新的描述。然后，这被用来证明吉里单子作为遗忘函子的共密度单子从凸集的某些类别和仿射映射到可测量空间的类别。
The Giry monad on the category of measurable spaces sends a space to a space of all probability measures on it. There is also a finitely additive Giry monad in which probability measures are replaced by finitely additive probability measures. We give a characterisation of both finitely and countably additive probability measures in terms of integration operators giving a new description of the Giry monads. This is then used to show that the Giry monads arise as the codensity monads of forgetful functors from certain categories of convex sets and affine maps to the category of measurable spaces.