On a covering property of convex sets

H. Groemer
1976 Proceedings of the American Mathematical Society  
Let [Kx, K2, ■ ■ ■ } be a class of compact convex subsets of euclidean M-space with the property that the set of their diameters is bounded. It is shown that the sets A, can be rearranged by the application of rigid motions so as to cover the total space if and only if the sum of the volumes of all the sets A, is infinite. Also, some statements regarding the densities of such coverings are proved.
doi:10.1090/s0002-9939-1976-0412970-2 fatcat:wunteavrarguzbk77zb4wdqoou