This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality between measures and measurable functions. A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels. The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic coherent spaces. The orthogonality is formulated by a Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated. As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.

翻译：摘要：本文通过引入两个新颖要素——（i）测度论中自然出现的线性指数余单子，以及（ii）测度与可测函数之间的连续正交性，研究了概率一致空间的随机构造。我们在转移核的对称幺半范畴上构造了一个线性指数余单子，将Panangaden随机关系中的马尔可夫核放宽为s-有限核。该模型支持基于测度与可测函数之间积分的正交性，可视为Girard-Danos-Ehrhard概率一致空间线性对偶的连续扩展。该正交性通过Hyland-Schalk双胶合构造形式化，我们建立的测度论幺半余单子结构可适配其中。作为可数可测空间上的应用，我们得到了一个dagger紧闭合范畴，其双胶合构造导出了熟悉的概率一致空间范畴。