TL;DR
This paper introduces a new algebraic and analytic framework called dimension structures, generalizing Hausdorff dimension and measure, with numerous examples and foundational properties explored.
Contribution
It presents a novel generalization of Hausdorff dimension and measure through the concept of dimension structures, expanding the theoretical landscape.
Findings
Many examples illustrating the new structures
Basic properties and relations analyzed
Potential applications in geometric measure theory
Abstract
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.