Inequality measures are quantitative measures that take values in the unit interval, with a zero value characterizing perfect equality. Although originally proposed to measure economic inequalities, they can be applied to several other situations, in which one is interested in the mutual variability between a set of observations, rather than in their deviations from the mean. While unidimensional measures of inequality, such as the Gini index, are widely known and employed, multidimensional measures, such as Lorenz Zonoids, are difficult to interpret and computationally expensive and, for these reasons, are not much well known. To overcome the problem, in this paper we propose a new scaling invariant multidimensional inequality index, based on the Fourier transform, which exhibits a number of interesting properties, and whose application to the multidimensional case is rather straightforward to calculate and interpret.

翻译：不平等度量是取值于单位区间的定量指标，其中零值表征完全平等。尽管最初是为衡量经济不平等而提出，但此类指标可广泛应用于其他情景——这些情景关注的是观测值集合间的相互变异程度，而非其与均值的偏离。虽然基尼系数等单维不平等度量已被广泛认知和应用，但洛伦兹区域体等多维度量因解释困难、计算成本高昂而鲜为人知。为解决此问题，本文提出一种基于傅里叶变换的新型尺度不变多维不平等指数，该指数具备若干优良性质，其多维情形的计算与解释也相当直观简便。