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

 

Symmetric and ordinary differentiation


Authors: C. L. Belna, M. J. Evans and P. D. Humke
Journal: Proc. Amer. Math. Soc. 72 (1978), 261-267
MSC: Primary 26A24
MathSciNet review: 507319
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Abstract: In 1927, A. Khintchine proved that a measurable symmetrically differentiable function f mapping the real line R into itself is differentiable in the ordinary sense at each point of R except possibly for a set of Lebesgue measure zero. Here it is shown that this exceptional set is also of the first Baire category; even more, it is shown to be a $ \sigma $-porous set of E. P. Dolženko.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0507319-2
PII: S 0002-9939(1978)0507319-2
Keywords: Dini derivates, symmetric derivates, $ \sigma $-porosity, metric density, monotonicity
Article copyright: © Copyright 1978 American Mathematical Society