HOLDER CONTINUITY AND DIFFERENTIABILITY ON CONVERGING SUBSEQUENCES

摘要

It is shown that an arbitrary function from DR n to R m will become C 0,α continuous in almost every x ∈ D after restriction to a certain subset with limit point x.For n ≥ m differentiability can be obtained.Examples show the H¨older exponent α = min{1,n/ m } is optimal.