Discontinuities of approximating measures on constant width sets (Q1891450)

Let \(\nu_\delta(I)\) be the approximating measure, obtained with closed \(\delta\)-coverings, of the one-dimensional Hausdorff measure of a set \(I\subset {\mathbf R}^2\). The paper deals with the function \(s_\delta(I)= \nu_{\delta-}(I)- \nu_\delta(I)\), where \(\nu_{\delta- }(I)\) is the limit of \(\nu_t(I)\) as \(t\uparrow \delta\). In particular, \(s_\delta(\partial K)\) and \(s_\delta(K)\) are studied for a set \(K\) of constant width.