For encompassing the limitations of probabilistic coherence spaces which do not seem to provide natural interpretations of continuous data types such as the real line, Ehrhard and al. introduced a model of probabilistic higher order computation based on (positive) cones, and a class of totally monotone functions that they called "stable". Then Crubill{\'e} proved that this model is a conservative extension of the earlier probabilistic coherence space model. We continue these investigations by showing that the category of cones and linear and Scott-continuous functions is a model of intuitionistic linear logic. To define the tensor product, we use the special adjoint functor theorem, and we prove that this operation is and extension of the standard tensor product of probabilistic coherence spaces. We also show that these latter are dense in cones, thus allowing to lift the main properties of the tensor product of probabilistic coherence spaces to general cones. Last we define in the same way an exponential of cones and extend measurability to these new operations.

中文翻译：

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关于锥体的线性结构

包含概率相干空间的局限性，这些空间似乎不能提供对连续数据类型（如实数线）的自然解释，Ehrhard 等。介绍了一种基于（正）锥的概率高阶计算模型，以及一类被他们称为“稳定”的完全单调函数。然后 Crubill{\'e} 证明了这个模型是早期概率相干空间模型的保守扩展。我们通过证明锥体和线性和斯科特连续函数的范畴是直觉线性逻辑的模型来继续这些研究。为了定义张量积，我们使用了特殊的伴随函子定理，我们证明了这个操作是概率相干空间的标准张量积的扩展。我们还表明，后者在锥体中是密集的，因此可以将概率相干空间的张量积的主要属性提升到一般锥体。最后，我们以相同的方式定义圆锥指数，并将可测量性扩展到这些新操作。