The history of uniform convergence is typically focused on the contributions of Cauchy, Seidel, Stokes, and Björling. While the mathematical contributions of these individuals to the concept of uniform convergence have been much discussed, Weierstrass is considered to be the actual inventor of today’s concept. This view is often based on his well-known article from 1841. However, Weierstrass’s works on a rigorous foundation of analytic and elliptic functions date primarily from his lecture courses at the University of Berlin up to the mid-1880s. For the history of uniform convergence, these lectures open up an independent branch of development that is disconnected from the approaches of the previously mentioned authors; to my knowledge, Weierstraß never explicitly referred to Cauchy’s continuity theorem (1821 or 1853) or to Seidel’s or Stokes’s contributions (1847). In the present article, Weierstrass’s contributions to the development of uniform convergence will be discussed, mainly based on lecture notes made by Weierstrass’s students between 1861 and the mid-1880s. The emphasis is on the notation and the mathematical rigor of the introductions to the concept, leading to the proposal to re-date the famous 1841 article and thus Weierstrass’s first introduction of uniform convergence.

统一收敛的历史通常集中在柯西，塞德尔，斯托克斯和比约林的贡献上。尽管已经讨论了这些人对统一收敛概念的数学贡献，但Weierstrass被认为是当今概念的实际发明者。这种观点通常基于他在1841年发表的著名文章。但是，Weierstrass在严格的解析和椭圆函数基础上的作品主要源于他在柏林大学的讲课直至1880年代中期。对于统一收敛的历史，这些讲座打开了一个独立的发展分支，与前面提到的作者的方法脱节。据我所知，Weierstraß从未明确提及柯西的连续性定理（1821或1853）或塞德尔或斯托克斯的贡献（1847）。在本文中，将主要基于Weierstrass的学生在1861年至1880年代中期之间所做的演讲笔记，讨论Weierstrass对统一收敛发展的贡献。重点在于对该概念的介绍的概念和数学上的严谨性，从而提出了重新命名1841年著名文章的建议，从而使Weierstrass首次引入了统一收敛。