Problem concerning the Lebesgue density at a point (Q2772762)

Author discusses some open problems connected with duality between Lebesgue measure and Baire category on the real line. The main of them is to find a satisfactory definition of a category density of a set \(A\) at a point \(x_0\). ``Satisfactory'' means a scheme for an abstract \(\sigma\)-algebra and a \(\sigma\)-ideal, which for a \(\sigma\)-algebra of measurable sets and a \(\sigma\)-ideal of null sets gives the ordinary density of a set at a point.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00067].