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On Continuous Functions which are Partially Differentiable Almost Everywhere

Published online by Cambridge University Press:  20 November 2018

L.V. Toralballa
L.V. Toralballa*
Affiliation:
New York University, BronxN. Y.
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In the theory of surface area one meets situations where a function z = f(x, y) which is defined and continuous on a closed rectangle E, is partially differentiable on E except on a subset of E of Lebesgue measure zero.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 668 - 672
Copyright
Copyright © Canadian Mathematical Society 1969

References

* Such functions are easy to construct. One takes a continuously partially differentiable function and merely "flattens " (i.e., replaces by a plane) a suitable sequence of subsets of S in a neighborhood of (P, f(P)).