• Corpus ID: 208248175

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

@article{Guo2019OnCM,
  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},
  year={2019}
}
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. 
View PDF on arXiv

References

SHOWING 1-5 OF 5 REFERENCES
Fractal geometry - mathematical foundations and applications
TLDR
Applications and examples: fractals defined by transformations examples from number theory graphs of functions examples from pure mathematics dynamical systems iteration of complex functions-Julia sets random fractals Brownian motion and Brownian surfaces multifractal measures physical applications.
On the Dimension of Iterated Sumsets
Let A be a subset of the real line. We study the fractal dimensions of the k-fold iterated sumsets kA, defined as $$kA =\{ {a}_{1} + \cdots + {a}_{k} : {a}_{i} \in A\}.$$ We show that for any…
Fractals in Probability and Analysis
TLDR
Central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem.
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