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Proceedings of the American Mathematical Society

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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: 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.


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

  • [1] 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 16, 344. MR 0064849 (16:344d)
  • [2] A. Sard, Images of critical sets, Ann. of Math. (2) 68 (1958), 247-259. MR 20 #6499. MR 0100063 (20:6499)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0260940-4
Keywords: Hausdorff measure, contiguous intervals, modulus of continuity
Article copyright: © Copyright 1970 American Mathematical Society

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