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，现有文献难以找到超越“依赖=非独立”这一自明之理的正式定义。这种缺失导致“依赖”一词及其衍生用法被模糊而不加区分地用于描述多种不同的概念，引发了诸多矛盾。例如，经典的皮尔逊相关系数、斯皮尔曼相关系数或肯德尔相关系数被广泛视为重要的“依赖度量”，但在变量间存在确定性关系时，这些系数仍可能返回0，显然并未真正度量依赖。本文认为，对这一基础性议题的研究若采用更为严谨的框架将有所裨益，因此提出了在同一概率空间上定义的两个随机变量之间依赖关系的一般性定义。该定义既足够自然以契合直觉，又足够精确以明确识别双变量分布依赖结构的“普适”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普适表示的依赖度量思想，证明其满足Rényi公设。