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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Measurability of partial derivatives

Authors: Moshe Marcus and Victor J. Mizel
Journal: Proc. Amer. Math. Soc. 63 (1977), 236-238
MSC: Primary 26A54
MathSciNet review: 0437696
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Abstract: Let f be a real function defined in $ {R_n}$. In this note we give a sufficient condition in order that the set of points where the partial derivative $ \partial f/\partial {x_i}$ exists is Lebesgue measurable and $ \partial f/\partial {x_i}$ is a measurable function on this set. This result unifies and extends a number of previous results.

References [Enhancements On Off] (What's this?)

  • [1] U. S. Haslam-Jones, Derivative planes and tangent planes of a measurable function, Quart. J. Math. Oxford 3 (1932), 120-132.
  • [2] James Serrin, On the differentiability of functions of several variables, Arch. Rational Mech. Anal. 7 (1961), 359–372. MR 0139700,
  • [3] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095

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Article copyright: © Copyright 1977 American Mathematical Society

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