Abstract
For a moving convex cylinder inR n, which is congruent to a given one, one considers the intersection with a given convex body and projects this intersection orthogonally into a generating subspace of the cylinder. The result of the note, which generalizes an earlier formula of Matheron, gives the mean value, with respect to the integral geometric measure on a space of congruent cylinders, of the Minkowski quermass-integrals of the resulting convex bodies.
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References
Davy P.,Projected thick sections through multi-dimensional particle aggregates, J. Appl. Prob.,13 (1976), 714–722. Correction: J. Appl. Prob.,15 (1978), 456.
Hadwiger H.,Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer, Berlin, Göttingen and Heidelberg, 1957.
Matheron G.,La formule de Crofton pour les sections épaisses, J. Appl. Prob.,13 (1976), 707–713.
Miles R. E.,On estimating aggregate and overall characteristics from thick sections by transmission microscopy, Proc. 4-th International Congress for Stereology. National Bureau of Standards Special Publication,431 (1976), 3–12.
Santaló L. A.,Integral geometry and geometric probability, Encyclopedia of Mathematics and its Applications I, Addison-Wesley, Reading, Mass., 1976.
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Schneider, R. Crofton's formula generalized to projected thick sections. Rend. Circ. Mat. Palermo 30, 157–160 (1981). https://doi.org/10.1007/BF02845135
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DOI: https://doi.org/10.1007/BF02845135