Abstract In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: Montes et al. (2015) [13] . The main tools we develop in order to do so are: (1) a theory on quasi-distributions based on an idea presented in a paper by R. Nelsen with collaborators; (2) starting from what is called (bivariate) p-box in the above mentioned paper we propose some new techniques based on what we call restricted (bivariate) p-box; and (3) a substantial extension of a theory on coherent imprecise copulas developed by M. Omladic and N. Stopar in a previous paper in order to handle coherence of restricted (bivariate) p-boxes. A side result of ours of possibly even greater importance is the following: Every bivariate distribution whether obtained on a usual σ-additive probability space or on an additive space can be obtained as a copula of its margins meaning that its possible extraordinariness depends solely on its margins. This might indicate that copulas are a stronger probability concept than probability itself.

中文翻译：

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不精确设置中的全标度 Sklar 定理

摘要 在本文中，我们对发表在本期刊上的一篇论文的主要结果进行了令人惊讶的普遍扩展：Montes 等人。(2015) [13]。我们为此开发的主要工具是： (1) 基于 R. Nelsen 与合作者在论文中提出的想法的准分布理论；(2) 从上面提到的论文中所谓的（双变量）p-box 开始，我们提出了一些基于我们所说的受限（双变量）p-box 的新技术；(3) M. Omladic 和 N. Stopar 在之前的论文中开发的相干不精确 copula 理论的实质性扩展，以处理受限（双变量）p-box 的相干性。我们可能更重要的一个附带结果如下：无论是在通常的 σ 可加概率空间还是在可加空间上获得的每个二元分布都可以作为其边缘的联结获得，这意味着其可能的非凡性仅取决于其边缘。这可能表明 copula 是一个比概率本身更强的概率概念。