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jAjZAjuixuiyj jxyjC1 jBjZBxjuixuzj jxzjdz1 jBjZByjuiyuixj jyxjdyCMDuxMDuyTheTheoremfollowsbytakingthesupremumoveri12 Corollary1For0thereexistsav2LipRk

jAjZAjui(x)ui(y)j jxyjC1 jBjZB(x)jui(x)u(z)j jxzjdz+1 jBjZB(y)jui(y)ui(x)j jyxjdyCMDu(x)+MDu(y):TheTheoremfollowsbytakingthesupremumoveri=1;2;:::. Corollary1.For0thereexistsav2Lip(Rk

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