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Abstract
It is a classical question in convex geometry whether there exists a σ-finite Borel measure on the space of convex bodies such that every open subset has positive measure. In this paper we give a positive answer by introducing a class of measures with the desired feature and additional invariance properties which are (in a certain sense) strongest possible.
Received: 2008-03-31
Revised: 2008-08-31
Published Online: 2010-04-12
Published in Print: 2010-July
© de Gruyter 2010