A note on simultaneous polar and Cartesian decomposition
Résumé
We study measures on R(n) which are product measures for the usual Cartesian product structure of R(n) as well as for the polar decomposition of R(n) induced by a convex body. For finite atomic measures and for absolutely continuous measures with density dmu/dx = e(-V(x)) where V is locally integrable, a complete characterization is presented.