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

On the continuity of functions in $ W\sp{1}\sb{p}$ which are monotonic in one direction


Author: Casper Goffman
Journal: Proc. Amer. Math. Soc. 42 (1974), 581-582
MSC: Primary 26A54; Secondary 46E35
MathSciNet review: 0327998
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Abstract: It was previously shown that, for $ n = 2$, if f is such that its distribution derivatives are measures, and f is monotonically nondecreasing in one variable for almost all values of the other variable then f is equivalent to a continuous function. This is now shown to be false for $ n > 2$. It is true for $ f \in W_p^1,p > n - 1$ and may be false for $ f \in W_{n - 1}^1$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0327998-9
PII: S 0002-9939(1974)0327998-9
Article copyright: © Copyright 1974 American Mathematical Society