The Kolmogorov–Riesz compactness theorem
Harald Hanche-Olsen and Helge Holden
Abstract: We show that the Arzelą–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.