Is it possible to define a coefficient of correlation which is (a) as simple
as the classical coefficients like Pearson's correlation or Spearman's
correlation, and yet (b) consistently estimates some simple and interpretable
measure of the degree of dependence between the variables, which is 0 if and
only if the variables are independent and 1 if and only if one is a measurable
function of the other, and (c) has a simple asymptotic theory under the
hypothesis of independence, like the classical coefficients? This article
answers this question in the affirmative, by producing such a coefficient. No
assumptions are needed on the distributions of the variables. There are several
coefficients in the literature that converge to 0 if and only if the variables
are independent, but none that satisfy any of the other properties mentioned
above.

本文回答了一个问题：是否可能定义一个与经典相关系数（如 Pearson's correlation or Spearman's correlation）一样简单的相关系数，并且能够一致估计出某种简单可解释的度量变量之间相互依赖程度的度量，满足该度量当且仅当变量是独立的时候为 0，且当且仅当其中一个是另一个的可测函数时为 1，且在独立假设下具有简单的渐近理论，并通过提出这样一个系数来肯定这一点，而在该文中，变量的分布不需要做出任何假设。