Starting from the notion of a multidistance, we formalize, through a suitable system of axioms, the concept of an inequality measure defined on a nonempty set with no additional structure implemented a priori. Among inequality measures, apart from multidistances we pay special attention to dispersions, and study their main features. Classical concepts will be generalized to this abstract setting. Multidistances are then revisited, and some new methods to generate them are implemented. A wide spectrum of interdisciplinary applications is outlined in the final section.

中文翻译：

---

抽象集上的多距离和不等式测度：一种公理化方法

从多距离的概念开始，我们通过合适的公理系统形式化了在非空集上定义的不等式测度的概念，而没有先验实现的附加结构。在不等式度量中，除了多距离之外，我们特别关注离散度，并研究它们的主要特征。经典概念将被推广到这个抽象的环境。然后重新审视多距离，并实现了一些生成它们的新方法。最后一部分概述了广泛的跨学科应用。