Finitely additive functionals in the space of planes. II (Q1374362)

In Part I [ibid. 29, 3-51 (1994; Zbl 0839.53053)], \textit{R. V. Ambartzumyan} and \textit{V. K. Oganyan} started the study of valuations on a certain ring \(U\) of subsets of the space \(\mathbb {E}\) of planes in \(\mathbb {R}^3\) as a tool to generate signed measures in the space \(\mathbb {E}\). In this paper, the authors give a complete solution to a problem posed there, finding necessary and sufficient conditions for a ``flag density'' to generate a signed measure in the space \(\mathbb {E}\).