Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term 'dependence' and its declination to be used vaguely and indiscriminately for qualifying a variety of disparate notions, leading to numerous incongruities. For example, the classical Pearson's, Spearman's or Kendall's correlations are widely regarded as 'dependence measures' of major interest, in spite of returning 0 in some cases of deterministic relationships between the variables at play, evidently not measuring dependence at all. Arguing that research on such a fundamental topic would benefit from a slightly more rigid framework, this paper suggests a general definition of the dependence between two random variables defined on the same probability space. Natural enough for aligning with intuition, that definition is still sufficiently precise for allowing unequivocal identification of a 'universal' representation of the dependence structure of any bivariate distribution. Links between this representation and familiar concepts are highlighted, and ultimately, the idea of a dependence measure based on that universal representation is explored and shown to satisfy Renyi's postulates.

翻译：依赖性无疑是统计学中的核心概念。然而，在文献中难以找到超越不言自明的“依赖性=非独立性”的形式化定义。这一缺失导致“依赖性”一词及其衍生词被模糊且不加区分地用于描述各种不同的概念，从而引发诸多矛盾。例如，经典的皮尔逊、斯皮尔曼或肯德尔相关系数通常被视为重要的“依赖性度量”，尽管在某些情况下，当变量之间存在确定性关系时，这些度量返回值为零，显然并未实际度量依赖性。本文认为，这一基础性主题的研究若能采用更为严谨的框架将有所裨益，并提出一种关于同一概率空间上两个随机变量之间依赖性的通用定义。该定义既足够自然以符合直觉，又足够精确，可明确识别任何二元分布依赖性结构的“通用”表示。本文还强调了该表示与常见概念之间的关联，并最终探讨了基于该通用表示的依赖性度量思想，证明其满足Rényi的公设条件。