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A thin set of lines

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Abstract

Examples are given of functionsf(x) taking [0,1] into, or indeed onto, [0,1] in such a way that two dimensional measure of the set consisting of all points on all the straight line segments connecting (x, 0) to (f(x), 1) is zero.

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References

  1. F. Herzog and G. Piranian,On the univalence of functions whose derivative has a positive real part, Proc. Amer. Math. Soc.2 (1951), 625–633.

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  2. J. P. Kahane,Trois notes sur les ensembles parfait lineares, Enseignement Math.15 (1969), 185–192.

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Authors
  1. J. R. Kinney
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Kinney, J.R. A thin set of lines. Israel J. Math. 8, 97–102 (1970). https://doi.org/10.1007/BF02771304

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  • DOI: https://doi.org/10.1007/BF02771304

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