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：依赖无疑是统计学中的核心概念。然而，在文献中很难找到超越"依赖=非独立"这一自我定义的形式化定义。这种缺失导致了"依赖"及其派生术语被模糊且不加区分地用于描述各种不同的概念，从而引发诸多不一致。例如，经典的皮尔逊、斯皮尔曼或肯德尔相关系数被广泛视为重要的"依赖度量"，但它们在变量间存在确定性关系时仍可能返回0，显然并未真正度量依赖。本文认为，对这一基础性问题的研究若能建立在更严谨的框架之上将有所裨益，因此提出了一个关于定义在同一概率空间上的两个随机变量之间依赖的通用定义。该定义既足够直观以符合直觉，又足够精确以确保能够明确识别任意二元分布依赖结构的"普适"表示。本文重点阐述了该表示与已知概念之间的联系，并最终探讨了基于该普适表示的依赖度量思想，证明其满足Renyi公设。