ScholarLens Back to search
2019•arXiv (Cornell University)Open access

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

Shaoming Guo, Tian Lan, Yakun Xi

Open full text 0 citations

Abstract

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.

Open-access reader

About this research paper

What this paper is about

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.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

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.

Key concepts: Convexity, Urysohn and completely Hausdorff spaces, Hausdorff space, Mathematics, Hausdorff distance, Regular polygon, Hausdorff measure, Borel measure

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets — Research Paper | ScholarLens