Raguso, Grazia; Rella, Luigia Density of a family of linear varieties. (English) Zbl 1123.53038 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 45, 143-152 (2006). Summary: The measurability of the family, made up of the family of plane pairs and the family of lines in 3-dimensional space \(A_3\), is stated and its density is given. MSC: 53C65 Integral geometry 28A75 Length, area, volume, other geometric measure theory Keywords:plane pairs; lines; density × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Chern S. S.: Sur les invariant integràus en géométrie. Sci. Repts. Nat., Tsing-Hua Univ., A 4 (1940), 85-95. [2] Cirlincione L.: On a family of varietes not satisfyng Stoka ’s measurability condition. Cahieres de Topologie et Géométrie Différentielle 24, 2 (1983), 145-154. [3] Crofton W. K.: On the theory of local probability, applied to straigth lines drawn at random in a plane; the method used being also extended to the proof of certain theorem in the integral calculus. Phil. Trans. R. Soc. London 158 (1869), 139-187. [4] Deltheil R.: Probabilités géométriques, nel Traité du calcul dès probabilités, de ses application. : Diretto da E. Borel, v. II, f.II (Paris, Gauthier-Villar). 1926. [5] Dulio P.: Restriction of measure on subfamlies. Atti del V Italiano Convegno di Geometria Integrale, Probabilità Geometriche e Corpi Convessi, Rend. Circ. Mat., Palermo, 1995. [6] Dulio P.: Some results on the Integral Geometry of unions of indipendent families. Rev. Colombiana Mat. 31, 2 (1997), 99-108. · Zbl 0918.60010 [7] Raguso G., Rella L.: Sulla misurabilità della famiglia delle coppie di sfere ortogonali. Suppl. Rend. Circ. Mat. di Palermo 41, 2 (1996), 186-94. [8] Raguso G., Rella L.: Sulla misurabilità delle coppie di ipersfere ortogonali di \(E_{n}\). Seminarberitche, Fachbereich Mathematik, Feruniversität, Hagen, 54 (1996), 154-164. [9] Santaló L. A.: Integral Geometry in projective and affiine spaces. Ann. of Math. 51, 2 (1950), 739-755. · Zbl 0041.31201 [10] Stoka M. I.: Geometria Integrale in uno spazio euclideo \(R^{n}\). Boll. Un. Mat. Ital. 13 (1958), 470-485. · Zbl 0088.14602 [11] Stoka M. I.: Géométrie Intégrale. : Mem. Sci. Math. 165, Gauthier-Villars, Paris. 1968. [12] Stoka M. I.: La misurabilità della famiglia delle ipersfere nello spazio proiettivo \(P_{n}\). : Atti dell’ Acc. di Scienze Lettere e Arti di Palermo, Serie IV, Vol. XXXVI, Parte I. 1976-77. [13] Stoka M. I.: Probabilità e Geometria. : Herbita Editrice, Palermo. 1982. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.