21. The uniform norm defines the topology of uniform convergence of functions on " X ". 22. The uniform structures allow one to talk about notions such as uniform continuity and uniform convergence on topological groups. 23. A central goal in designing a consistent, using the uniform convergence properties of empirical quantities to their means. 24. The situation is rather bad for equidistant nodes, in that uniform convergence is not even guaranteed for infinitely differentiable functions. 25. His dissertation, " On Uniform Convergence of Families of Sequences of Random Variables ", was written under Michel Lo�ve. 26. Uniform convergence implies both local uniform convergence and compact convergence, since both are local notions while uniform convergence is global.27. Uniform convergence implies both local uniform convergence and compact convergence, since both are local notions while uniform convergence is global. 28. Uniform convergence implies both local uniform convergence and compact convergence, since both are local notions while uniform convergence is global. 29. So, first of all how do we conclude that the topology is simply the product / local uniform convergence topology? 30. Let \ partial G act as a discrete uniform convergence group on a compact metrizable space M with no isolated points.
