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Proceedings of the American Mathematical Society

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A note on a theorem of Gehring and Lehto

Author: A. G. Fadell
Journal: Proc. Amer. Math. Soc. 49 (1975), 195-198
MSC: Primary 26A54; Secondary 30A60
MathSciNet review: 0367132
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Abstract: The concept of mesh approximate differential is defined as a modification of regular approximate differential. It is shown that for open continuous real-valued maps on open sets in $ n$-space the concepts of mesh approximate differentiability and total differentiability are equivalent, and the Gehring-Lehto theorem is obtained as a corollary by a sharpening of a known theorem on regular approximate differentials.

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Keywords: Total differential, regular approximate differential, mesh approximate differential, open continuous mapping
Article copyright: © Copyright 1975 American Mathematical Society

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