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Tangential measure on the set of convex infinite cylinders

Published online by Cambridge University Press:  24 August 2016

Ursula Maria Molter
Ursula Maria Molter*
Affiliation:
Universidad de Buenos Aires
*
∗Postal address: Department of Mathematics, Facultad de Cs. Exactas y Nat., Universidad de Buenos Aires, Ciudad Universitaria, (1428) Capital federal, Argentina.
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Abstract

We find a ‘natural' measure on the set of convex infinite cylinders touching a convex body K in En. Using the curvature measures, we can calculate the probability that a convex infinite cylinder and a convex body K are tangent in some previously determined regions. As a particular case we obtain a measure on all q-planes touching K.

Keywords

TANGENTIAL PROBABILITIESCURVATURE MEASURESHAAR MEASURESTEINER FORMULA
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 961 - 972
Copyright
Copyright © Applied Probability Trust 1986 

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References

Firey, W. J. (1974) Kinematic measure for sets of support figures. Mathematika 21, 270–281.CrossRefGoogle Scholar
Mcmullen, P. (1974) A dice probability problem. Mathematika 21, 193–198.Google Scholar
Santaló, L. A. (1976) Integral Geometry and Geometric Probability. Addison-Wesley, Reading, Mass.Google Scholar
Schneider, R. (1978a) Curvature measures of convex bodies. Ann. Mat. Pura Appl. 116, 101–134.Google Scholar
Schneider, R. (1978b) Kinematic measures for sets of colliding convex bodies. Mathematika 25, 1–12.CrossRefGoogle Scholar
Schneider, R. (1979) Integralgeometrie. Vorlesungen an der Universität Freiburg im sommer-semester 1979.Google Scholar
Weil, W. (1979) Berührwahrscheinlichkeiten für konvexe Körper. Z. Wahrscheinlichkeitsth. 48, 327–338.Google Scholar
Weil, W. (1981) Zufällige Berührung konvexer Körper durch q-dimensionale Ebenen. Result. Math. 4, 84–101.Google Scholar