A remark on wedge densities in \(\mathbb{R}^ 3\) (Q1896858)

A flag is a pair \((l,e)\), where \(e\) is a plane in \(\mathbb{R}^3\) and \(l \subset e\) is a line which contains the origin. A measure \(\mu\) on the space of all planes in \(\mathbb{R}^3\) induces a symmetric measure \(\mu^*\) on the unit sphere \(\Omega^2\). The author characterizes smooth functions \(\rho(l,e)\) on the space of flags which can be obtained as wedge density of a measure \(\mu\) on the space of all planes, i.e. \[ \rho (l,e) = {1\over 2\pi} \int_{\Omega^2} \sin^2 \alpha((l,e),\omega) d\mu^* (\omega), \] where \(\alpha ((l, e), \omega)\) is the angle between \(l\) and the line obtained by intersection \(l\) and the plane orthogonal to \(\omega\).