| Abstract: | In spite of the Lebesgue density theorem, there is a positive ({delta}) such that, for every measurable set ({A subset mathbb{R}}) with ({lambda (A) > 0}) and ({lambda (mathbb{R} setminus A) > 0}), there is a point at which both the lower densities of ({A}) and of the complement of ({A}) are at least ({delta}). The problem of determining the supremum of possible values of this ({delta}) was studied by V. I. Kolyada, A. Szenes and others. It seems that the authors considered this quantity a feature of density. We show that it is connected rather with a choice of a differentiation basis. |
