O integrální geometrii
The measurable sets of pairs of intersecting non-isotropic straight lines of type and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.
We study the measurability of sets of pairs of straight lines with respect to the group of motions in the simply isotropic space by solving PDEs. Also some Crofton type formulas are obtained for the corresponding densities.
In this paper we prove that the non degenerate conic sections' family in the projective space is measurable.