Representation of linear sets as critical sets
Author:
Robert Kaufman
Journal:
Proc. Amer. Math. Soc. 25 (1970), 884-889
MSC:
Primary 26.35
DOI:
https://doi.org/10.1090/S0002-9939-1970-0260940-4
MathSciNet review:
0260940
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Abstract | References | Similar Articles | Additional Information
Abstract: A class of linear sets investigated by Besicovitch and Taylor is related to the critical set of differentiable mappings of a specified degree of smoothness. An example is constructed to show that certain results on Hausdorff measure are nearly best-possible.
- A. S. Besicovitch and S. J. Taylor, On the complementary intervals of a linear closed set of zero Lebesgue measure, J. London Math. Soc. 29 (1954), 449–459. MR 64849, DOI https://doi.org/10.1112/jlms/s1-29.4.449
- Arthur Sard, Images of critical sets, Ann. of Math. (2) 68 (1958), 247–259. MR 100063, DOI https://doi.org/10.2307/1970246
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Keywords:
Hausdorff measure,
contiguous intervals,
modulus of continuity
Article copyright:
© Copyright 1970
American Mathematical Society