• Corpus ID: 208248175

On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets.

  title={On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets.},
  author={Shaoming Guo and Tian Lan and Yakun Xi},
  journal={arXiv: Classical Analysis and ODEs},
We give a complete characterization of the size of Borel sets that are mid-point convex but not (essentially) convex, in terms of their Hausdorff dimensions and Hausdorff measures. 


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Fractals in Probability and Analysis
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53706, USA E-mail address: shaomingguo2018@gmail.com Tian Lan: Department of Mathematics, The Chinese
  • 2018
E-mail address: 1155091994@link.cuhk.edu.hk
  • Yakun Xi: Department of Mathematics,
  • 1994