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PDF-Theorem:Supposethatfn:E!RconvergesuniformlyonEtoafunctionf.Supposethat

PDF-Theorem:Supposethatfn:E!RconvergesuniformlyonEtoafunctionf.Supposethat

Author : stefany-barnette | Published Date : 2016-08-18

3holdsforallx2ENowlookatfNThisfunctioniscontinuousatx0hencethereexistsa0sothatjxx0jx2EimpliesthatjfNxfNx0j 3Thenforanyx2Ejxx0jwehavejfxfx0jjfxfNxjjfNxfNx0jjfNx0

3holdsforallx2E.NowlookatfN.Thisfunctioniscontinuousatx0 hencethereexistsa0sothatjxx0j x2EimpliesthatjfN(x)fN(x0)j 3.Then foranyx2E jxx0j wehavejf(x)f(x0)jjf(x)fN(x)j+jfN(x)fN(x0)j+jfN(x0)

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Theorem:Supposethatfn:E!RconvergesuniformlyonEtoafunctionf.Supposethat: Transcript

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