| Title:
|
Density of a family of linear varietes (English) |
| Author:
|
Raguso, Grazia |
| Author:
|
Rella, Luigia |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
143-152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
integral geometry |
| MSC:
|
28A75 |
| MSC:
|
53C65 |
| idZBL:
|
Zbl 1123.53038 |
| idMR:
|
MR2321306 |
| . |
| Date available:
|
2009-08-21T07:06:38Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133451 |
| . |
| Reference:
|
[1] Chern S. S.: Sur les invariant integràus en géométrie.Sci. Repts. Nat., Tsing-Hua Univ., A 4 (1940), 85–95. MR 0004527 |
| Reference:
|
[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. MR 0710037 |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[6] Dulio P.: Some results on the Integral Geometry of unions of indipendent families.Rev. Colombiana Mat. 31, 2 (1997), 99–108. MR 1667592 |
| Reference:
|
[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. |
| Reference:
|
[8] Raguso G., Rella L.: Sulla misurabilità delle coppie di ipersfere ortogonali di $E_{n}$.Seminarberitche, Fachbereich Mathematik, Feruniversität, Hagen, 54 (1996), 154–164. |
| Reference:
|
[9] Santaló L. A.: Integral Geometry in projective and affiine spaces.Ann. of Math. 51, 2 (1950), 739–755. MR 0035046 |
| Reference:
|
[10] Stoka M. I.: Geometria Integrale in uno spazio euclideo $R^{n}$.Boll. Un. Mat. Ital. 13 (1958), 470–485. MR 0103516 |
| Reference:
|
[11] Stoka M. I.: Géométrie Intégrale. : Mem. Sci. Math. 165, Gauthier-Villars, Paris.1968. MR 0231336 |
| Reference:
|
[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. |
| Reference:
|
[13] Stoka M. I.: Probabilità e Geometria. : Herbita Editrice, Palermo.1982. |
| . |
