Ricerc@Sapienza

The convenient theoretical properties of the support function and the
Minkowski addition-based arithmetic have been shown to be useful when dealing
with compact and convex sets on Rp. However, both concepts present several drawbacks
in certain contexts. The use of the radial function instead of the support function
is suggested as an alternative to characterize a wider class of sets—the so-called
star-shaped sets—which contains the class of compact and convex sets as a particular
case. The concept of random star-shaped set is considered, and some statistics for
this kind of variable are shown. Finally, some measures for comparing star-shaped
sets are introduced.