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Proceedings of the American Mathematical Society

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

 

 

Strict essential minima


Author: R. J. O’Malley
Journal: Proc. Amer. Math. Soc. 33 (1972), 501-504
MSC: Primary 28A20; Secondary 26A54
MathSciNet review: 0291400
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Abstract: A simple proof is given of the fact that the set of strict essential minima of a real function of n variables is of measure zero. The proof uses only that a continuous function on a compact set has a maximum and the elementary fact, which seems to be new, that each set of positive measure contains a compact set which has positive upper density at each of its points.


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

  • [1] I. J. Good, The approximate local monotony of measurable functions, Proc. Cambridge Philos. Soc. 36 (1940), 9–13. MR 0001266
  • [2] Ákos Császár, Sur la structure des ensembles de niveau des fonctions réelles à deux variables, Acta Sci. Math. Szeged 15 (1954), 183–202 (French). MR 0064845
  • [3] Henry Blumberg, The measurable boundaries of an arbitrary function, Acta Math. 65 (1935), no. 1, 263–282. MR 1555405, 10.1007/BF02420947
  • [4] J. C. Burkill and U. S. Haslam-Jones, The derivates and approximate derivates of measurable functions, Proc. London Math. Soc. 32 (1931), 346-355.

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DOI: https://doi.org/10.1090/S0002-9939-1972-0291400-4
Article copyright: © Copyright 1972 American Mathematical Society