Geometriae Dedicata

, Volume 9, Issue 3, pp 299–306

On surface area measures of convex bodies

  • Wolfgang Weil

DOI: 10.1007/BF00181175

Cite this article as:
Weil, W. Geom Dedicata (1980) 9: 299. doi:10.1007/BF00181175


The set Lj of jth-order surface area measures of convex bodies in d-space is well known for j=d−1. A characterization of Lj was obtained by Firey and Berg. The determination of Lj, for j∈{2, ..., d−2}, is an open problem. Here we show some properties of Lj concerning convexity, closeness, and size. Especially we prove that the difference set LjLj is dense (in the weak topology) in the set of signed Borel measures on the unit sphere which have barycentre 0.

Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • Wolfgang Weil
    • 1
  1. 1.Inst. f. Math. StochastikAlbert-Ludwigs-UniversitätFreiburgW. Germany