Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A54

Retrieve articles in all journals with MSC: 26A54


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0437696-1
Article copyright: © Copyright 1977 American Mathematical Society