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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Symmetric semicontinuity implies continuity


Author: Jaromir Uher
Journal: Trans. Amer. Math. Soc. 293 (1986), 421-429
MSC: Primary 26A15; Secondary 26A24
MathSciNet review: 814930
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Abstract: The main result of this paper shows that, for any function, symmetric semicontinuity on a measurable set $ E$ implies continuity a.e. in $ E$ and, similarly, that symmetric semicontinuity on a set residual in $ R$ implies continuity on a set residual in $ R$. These propositions are used to prove more precise versions of the fundamental connections between symmetric and ordinary differentiability.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0814930-7
PII: S 0002-9947(1986)0814930-7
Article copyright: © Copyright 1986 American Mathematical Society