Since its introduction over 50 years ago, the concept of Mosco convergence has permeated through diverse areas of mathematics and applied sciences. These include applied analysis, the theory of partial differential equations, numerical analysis, and infinite dimensional constrained optimization, among others. In this paper we explore some of the consequences of Mosco convergence on applied problems that involve moving sets, with some historical accounts, and modern trends and features. In particular, we focus on connections with density of convex intersections, finite element approximations, quasi-variational inequalities, and impulse problems.

翻译：自50多年前引入以来,Mosco趋同的概念渗透到数学和应用科学的不同领域,其中包括应用分析、部分差异方程理论、数字分析和无限维度限制优化等。本文探讨了Mosco趋同在应用问题上的一些后果,这些问题涉及移动装置,并附有一些历史记录,以及现代趋势和特征。特别是,我们侧重于与 convex交叉密度、有限元素近似、准变量不平等和脉冲问题的联系。