Theorem:Supposethatfn:E!RconvergesuniformlyonEtoafunctionf.Supposethat - PPT Presentation
3holdsforallx2ENowlookatfNThisfunctioniscontinuousatx0hencethereexistsa0sothatjxx0jx2EimpliesthatjfNxfNx0j
3Thenforanyx2Ejxx0jwehavejfxfx0jjfxfNxjjfNxfNx0jjfNx0 ID: 451550
3holdsforallx2E.NowlookatfN.Thisfunctioniscontinuousatx0