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Proceedings of the American Mathematical Society
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.

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PII: S 0002-9939(1972)0291400-4
Article copyright: © Copyright 1972 American Mathematical Society

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