On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space

Adrijan Varbanov Borisov; Margarita Georgieva Spirova

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2009)

  • Volume: 48, Issue: 1, page 7-16
  • ISSN: 0231-9721

Abstract

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The measurable sets of pairs of intersecting non-isotropic straight lines of type β 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.

How to cite

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Borisov, Adrijan Varbanov, and Spirova, Margarita Georgieva. "On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 48.1 (2009): 7-16. <http://eudml.org/doc/35177>.

@article{Borisov2009,
abstract = {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.},
author = {Borisov, Adrijan Varbanov, Spirova, Margarita Georgieva},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Simply isotropic space; density; measurability; non-isotropic straight lines; Crofton-type formulas},
language = {eng},
number = {1},
pages = {7-16},
publisher = {Palacký University Olomouc},
title = {On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space},
url = {http://eudml.org/doc/35177},
volume = {48},
year = {2009},
}

TY - JOUR
AU - Borisov, Adrijan Varbanov
AU - Spirova, Margarita Georgieva
TI - On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2009
PB - Palacký University Olomouc
VL - 48
IS - 1
SP - 7
EP - 16
AB - 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.
LA - eng
KW - Simply isotropic space; density; measurability; non-isotropic straight lines; Crofton-type formulas
UR - http://eudml.org/doc/35177
ER -

References

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  1. Borisov, A., Integral geometry in the Galilean plane, Research work qualifying for a degree full-professor, Sofia, 1998. (1998) 
  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. (2006) MR2361199
  3. Deltheil, R., Sur la théorie des probabilité géométriques, Thése Ann. Fac. Sc. Univ. Toulouse 11 (1919), 1–65. (1919) MR1508362
  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). (1949) MR0082632
  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). (1964) MR0196037
  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). (1965) MR0213983
  7. Sachs, H., Ebene isotrope Geometrie, Friedr. Vieweg and Sohn, Braunschweig, 1987. (1987) Zbl0625.51001MR0908294
  8. Sachs, H., Isotrope Geometrie des Raumes, Friedr. Vieweg and Sohn, Braunschweig–Wiesbaden, 1990. (1990) Zbl0703.51001MR1059891
  9. Santaló, L. A., London, Integral Geometry and Geometric Probability, Addison-Wesley, London, 1976. (1976) MR0433364
  10. Stoka, M. I., Geometrie Integrala, Ed. Acad. RPR, Bucuresti, 1967. (1967) MR0217747
  11. Strubecker, K., Differentialgeometrie des isotropen Raumes I, Sitzungsber. Österr. Akad. Wiss. Wien 150 (1941), 1–53. (1941) MR0018957
  12. Strubecker, K., Differentialgeometrie des isotropen Raumes II, III, IV, V., Math. Z. 52 (1949), 525–573. (1949) MR0029201

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