Pathological planar shapes of any measure
Source: Admission to SNSB, 2002
October 4, 2019
Measure theoryreal analysis
Problem Statement
Present a family of subsets of the plane such that each one of its members is Lebesgue measurable, each one of its members intersects any circle, and the set of Lebesgue measures of all its members is the set of nonnegative real numbers.