Strong differentiability of Lipschitz functions
Author:
C. J. Neugebauer
Journal:
Trans. Amer. Math. Soc. 240 (1978), 295-306
MSC:
Primary 26A16; Secondary 46E35
DOI:
https://doi.org/10.1090/S0002-9947-1978-0489599-X
MathSciNet review:
489599
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Abstract | References | Similar Articles | Additional Information
Abstract: Let F be a differentiation basis in , i.e., a family of measurable sets S contracting to 0 such that
, where
is the Hardy-Littlewood maximal operator. For
, we let
be the complement of the Lebesgue set of f relative to F, and we show that
has
-capacity 0, where
is a capacity associated with
in much the same way as the Bessel capacity
is associated with
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1978-0489599-X
Keywords:
Lipschitz spaces,
Lipschitz capacity,
differentiation
Article copyright:
© Copyright 1978
American Mathematical Society