Analyticity of almost everywhere differentiable functions

Howard, Eric J.

doi:10.1090/S0002-9939-1990-1027093-9

Analyticity of almost everywhere differentiable functions
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by Eric J. Howard PDF

Proc. Amer. Math. Soc. 110 (1990), 745-753 Request permission

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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