Density of a family of linear varietes

Grazia Raguso; Luigia Rella

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 143-152
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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Raguso, Grazia, and Rella, Luigia. "Density of a family of linear varietes." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 143-152. <http://eudml.org/doc/32514>.

@article{Raguso2006,
abstract = {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.},
author = {Raguso, Grazia, Rella, Luigia},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {integral geometry; plane pairs; lines; density},
language = {eng},
number = {1},
pages = {143-152},
publisher = {Palacký University Olomouc},
title = {Density of a family of linear varietes},
url = {http://eudml.org/doc/32514},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Raguso, Grazia
AU - Rella, Luigia
TI - Density of a family of linear varietes
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 143
EP - 152
AB - 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.
LA - eng
KW - integral geometry; plane pairs; lines; density
UR - http://eudml.org/doc/32514
ER -

References

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  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. (1983) MR0710037
  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. (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. (1995) 
  6. Dulio P., Some results on the Integral Geometry of unions of indipendent families, Rev. Colombiana Mat. 31, 2 (1997), 99–108. (1997) MR1667592
  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. (1996) 
  8. Raguso G., Rella L., Sulla misurabilità delle coppie di ipersfere ortogonali di E n , Seminarberitche, Fachbereich Mathematik, Feruniversität, Hagen, 54 (1996), 154–164. (1996) 
  9. Santaló L. A., Integral Geometry in projective and affiine spaces, Ann. of Math. 51, 2 (1950), 739–755. (1950) MR0035046
  10. Stoka M. I., Geometria Integrale in uno spazio euclideo R n , Boll. Un. Mat. Ital. 13 (1958), 470–485. (1958) MR0103516
  11. Stoka M. I.: Géométrie Intégrale., Mem. Sci. Math. 165, Gauthier-Villars, Paris, 1968. MR0231336
  12. Stoka M. I.: La misurabilità della famiglia delle ipersfere nello spazio proiettivo ., 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. 

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