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

DOI:
https://doi.org/10.1090/S0002-9939-1990-1027093-9

MathSciNet review:
1027093

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-1990-1027093-9

Keywords:
-fine partition,
exceptional set,
lower derivate

Article copyright:
© Copyright 1990
American Mathematical Society