Strict essential minima
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- by R. J. O’Malley PDF
- Proc. Amer. Math. Soc. 33 (1972), 501-504 Request permission
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
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- Henry Blumberg, The measurable boundaries of an arbitrary function, Acta Math. 65 (1935), no. 1, 263–282. MR 1555405, DOI 10.1007/BF02420947 J. C. Burkill and U. S. Haslam-Jones, The derivates and approximate derivates of measurable functions, Proc. London Math. Soc. 32 (1931), 346-355.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 501-504
- MSC: Primary 28A20; Secondary 26A54
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291400-4
- MathSciNet review: 0291400