On lower density operators (Q6550095)

In classical density topologies, the interior of a Lebesgue measurable set \(A\) is a subset of its density points, and the set of all density points of \(A\) is a subset of the closure of \(A\).\N\NIn this paper, the authors focus on lower density operators and consider two examples of lower density operators for which the above property does not hold.\N\NTo define these examples, measure-preserving bijections on the real line are applied.\N\NIn the next section, the paper deals with the operation \(D\) in a measurable space which has the hull property, and investigates the relationship between \(D(A)\) and \(\Phi(A)\), where \(A\) is a Lebesgue measurable set.