ar X iv : m at h / 05 11 51 8 v 1 [ m at h . C A ] 2 1 N ov 2 00 5 SECOND ORDER DIFFERENTIABILITY OF REAL FUNCTIONS VIA
نویسنده
چکیده
We find an equivalent condition for a real function to be Lebesgue equivalent to a twice differentiable function. For that purpose, we introduce the notion of a V BG 1 2 function, which plays an analogous rôle for the second order differentiability as the classical notion of a V BG∗ function for the first order differentiability. In fact, for a function f : [a, b] → R, being Lebesgue equivalent to a twice differentiable function is the same as being Lebesgue equivalent to a differentiable function with a pointwise Lipschitz derivative. We also consider the case when the first derivative can be taken non-zero almost everywhere.
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