Bounds of Hausdorff measures of tame sets
Ta Le Loi, Phan Phien
TL;DR
This paper establishes bounds on Hausdorff measures for definable sets in o-minimal structures, providing explicit bounds for semi-algebraic and semi-Pfaffian cases based on combinatorial data.
Contribution
It introduces bounds for Hausdorff measures of tame sets and their fibers, with explicit bounds for semi-algebraic and semi-Pfaffian objects depending on combinatorial parameters.
Findings
Bounds for Hausdorff measures of definable sets
Explicit bounds for semi-algebraic sets
Explicit bounds for semi-Pfaffian sets
Abstract
In this paper we present some bounds of Hausdorff measures of objects definable in o-minimal structures: sets, fibers of maps, inverse images of curves of maps, etc. Moreover, we also give some explicit bounds for semi-algebraic or semi-Pfaffian cases, which depend only on the combinatoric data representing the objects involved.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Topological and Geometric Data Analysis