Generic properties of compact starshaped sets

Gruber, Peter M.; Zamfirescu, Tudor I.

doi:10.1090/S0002-9939-1990-0986649-X

Generic properties of compact starshaped sets
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by Peter M. Gruber and Tudor I. Zamfirescu PDF

Proc. Amer. Math. Soc. 108 (1990), 207-214 Request permission

Abstract:

A typical compact starshaped set in ${{\text {E}}^d}$ is "small" from the topological as well as from the measure theoretic viewpoint. We formulate this more explicitly in the paper by using the notions of porosity and Hausdorff dimension. Moreover, we see that the directions of the line segments in a typical compact starshaped set are many, but not too many.

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