Conjuntos de segmentos sobre superficies

Santaló, Lluís
The sets of segments randomly distributed on the plane have been recently investigated by COLEMAN [1] , [2] , PARKER-COWAN [3] and SANTALO [8] among others. In the present paper, we consider some qüestions analogous to that of PARKER-COWAN for sets of "geodèsic segments" on surfaces, in particular, sets of segments on the sphere and on the hyperbolic plane. We get the mean vàlues of the total length of the part of segments which are interior to a convex set K and the mean value of the intersection points of pairs of segments that are interior to K . For the hypertKJlic plane, we cunsider also the case of segments distributed on the plane according to a process of Poisson ​
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