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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Analyticity of almost everywhere differentiable functions


Author: Eric J. Howard
Journal: Proc. Amer. Math. Soc. 110 (1990), 745-753
MSC: Primary 26B05; Secondary 26E05, 30B40
MathSciNet review: 1027093
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Abstract: We develop a partitioning lemma (see Lemma 5) for superadditive set functions satisfying certain continuity conditions. This leads to a relatively simple proof of two theorems of A. S. Besicovitch on when a function of a complex variable that is continuous and differentiable outside of small exceptional sets is analytic (or almost everywhere equal to an analytic function).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1027093-9
PII: S 0002-9939(1990)1027093-9
Keywords: $ \delta $-fine partition, exceptional set, lower derivate
Article copyright: © Copyright 1990 American Mathematical Society