Summary
We compute the expected values of certain random variables associated with a random process of manifolds in R n by inserting certain general formulas of integral geometry into the definition of the moment measures of a point process.
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Berman, M.: Distance distributions associated with Poisson processes of geometric figures. J. Appl Probability 14, 195–199 (1977)
Coleman, R.: The distance from a given point to the nearest end of one member of a random process of linear segments. In Stochastic Geometry. Ed. Harding and Kendall pp. 192–201. New York: Wiley 1974
Fava, N., Santaló, L.A.: Plate and line segment processes, J. Appl. Probability 15, 494–501 (1978)
Groemer, H.: Eulersche Characteristic, Projectionen und Quermassintegrale. Math. Ann. 198, 23–56 (1972)
Hadwiger, H.: Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Berlin-Heidelberg-New York: Springer 1957
Krickeberg, K.: Moments of Point-processes. Stochastic Geometry. Ed. Harding and Kendall, pp. 89–113. New York: Wiley 1974
Lefschetz, S.: Introduction to Topology. Princeton University Press 1949
Parker, P., Cowan, R.: Some properties of line segment processes. J. Appl. Probability 13, 96–107 (1976)
Santaló, L.A.: Integralgeometrie 5, Exposés de Géométrie. Paris: Hermann 1936
Santaló, L.A.: Integral Geometry and Geometric Probability, Encyclopedia of Mathematics and its Applications. Reading, Mass.: Addison-Wesley 1976
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Dedicated to Professor Leopold Schmetterer on the occasion of his 60th Birthday
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Fava, N.A., Santaló, L.A. Random processes of manifolds in R n . Z. Wahrscheinlichkeitstheorie verw Gebiete 50, 85–96 (1979). https://doi.org/10.1007/BF00535675
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DOI: https://doi.org/10.1007/BF00535675