| Title:
|
On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space (English) |
| Author:
|
Borisov, Adrijan Varbanov |
| Author:
|
Spirova, Margarita Georgieva |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
7-16 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The measurable sets of pairs of intersecting non-isotropic straight lines of type $\beta $ 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. (English) |
| Keyword:
|
Simply isotropic space |
| Keyword:
|
density |
| Keyword:
|
measurability |
| MSC:
|
28A75 |
| MSC:
|
52A22 |
| MSC:
|
53C65 |
| idZBL:
|
Zbl 1203.53072 |
| idMR:
|
MR2641943 |
| . |
| Date available:
|
2010-02-11T13:47:30Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137502 |
| . |
| Reference:
|
[1] Borisov, A.: Integral geometry in the Galilean plane.Research work qualifying for a degree full-professor, Sofia, 1998. |
| Reference:
|
[2] Borisov, A. V., Spirova, M. G.: Crofton-type formulas relating sets of pairs of intersecting nonisotropic straight lines in the simply isotropic space.Tensor 67 (2006), 243–253. MR 2361199 |
| Reference:
|
[3] Deltheil, R.: Sur la théorie des probabilité géométriques.Thése Ann. Fac. Sc. Univ. Toulouse 11 (1919), 1–65. MR 1508362 |
| Reference:
|
[4] Drinfel’d, G. I.: On the measure of the Lie groups.Zap. Mat. Otdel. Fiz. Mat. Fak. Kharkov. Mat. Obsc. 21 (1949), 47–57 (in Russian). MR 0082632 |
| Reference:
|
[5] Drinfel’d, G. I., Lucenko, A. V.: On the measure of sets of geometric elements.Vest. Kharkov. Univ. 31, 3 (1964), 34–41 (in Russian). MR 0196037 |
| Reference:
|
[6] Lucenko, A. V.: On the measure of sets of geometric elements and thear subsets.Ukrain. Geom. Sb. 1, 3 (1965), 39–57 (in Russian). MR 0213983 |
| Reference:
|
[7] Sachs, H.: Ebene isotrope Geometrie.Friedr. Vieweg and Sohn, Braunschweig, 1987. Zbl 0625.51001, MR 0908294 |
| Reference:
|
[8] Sachs, H.: Isotrope Geometrie des Raumes.Friedr. Vieweg and Sohn, Braunschweig–Wiesbaden, 1990. Zbl 0703.51001, MR 1059891 |
| Reference:
|
[9] Santaló, L. A., London: Integral Geometry and Geometric Probability.Addison-Wesley, London, 1976. MR 0433364 |
| Reference:
|
[10] Stoka, M. I.: Geometrie Integrala.Ed. Acad. RPR, Bucuresti, 1967. MR 0217747 |
| Reference:
|
[11] Strubecker, K.: Differentialgeometrie des isotropen Raumes I.Sitzungsber. Österr. Akad. Wiss. Wien 150 (1941), 1–53. MR 0018957 |
| Reference:
|
[12] Strubecker, K.: Differentialgeometrie des isotropen Raumes II, III, IV, V.. Math. Z. 52 (1949), 525–573. MR 0029201 |
| . |
