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，在文献中难以找到一个超越不言自明的“依赖性=非独立性”的正式定义。这一缺失导致“依赖性”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，从而引发众多矛盾。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“依赖性度量”，尽管在变量之间存在确定性关系的情况下它们可能返回0，显然并未真正度量依赖性。本文认为，这一基础课题的研究将得益于一个更为严谨的框架，并提出了一种通用定义，用于描述定义在同一概率空间上的两个随机变量之间的依赖性。该定义既足够自然以符合直觉，又足够精确，能够明确识别任何二元分布依赖结构的“通用”表示。本文强调了该表示与常见概念之间的联系，并最终探索了基于该通用表示的依赖性度量思想，表明其满足Rényi公设。