Summary
Combinatorial formulae for the numbers of cells of subdivision, of varying dimensions, when hyperplanes in general position intersect an open convex set of ℝd, are derived. They coincide with basic formulae for the probabilities of combinations of events. The dual result is stated.
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I should like to thank a referee for drawing attention to the duality.
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Miles, R.E. A generalization of a formula of Steiner. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 375–378 (1982). https://doi.org/10.1007/BF00539837
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DOI: https://doi.org/10.1007/BF00539837