6533b86ffe1ef96bd12cd1f4

RESEARCH PRODUCT

A note on the distance set problem in the plane

Themis Mitsis

subject

Discrete mathematicsPlane (geometry)Applied MathematicsGeneral MathematicsMathematical analysisσ-finite measureMeasure (mathematics)Set (abstract data type)Simple (abstract algebra)Mathematics::Metric GeometryHausdorff measureOuter measureBorel measureMathematics

description

We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.

https://doi.org/10.1090/s0002-9939-01-06375-4