On a Problem Related to Sphere and Circle Packing
Themis Mitsis · Journal of the London Mathematical Society · 1999
The paper proves that a set which contains spheres centered at all points of a set of Hausdorff dimension greater than 1 must have positive Lebesgue measure. It also proves the corresponding result for circles, provided that the set of centers has Hausdorff dimension greater than 3/2.