(L^? center) are unique (when they exist), while the median (L¹ center) and mode (L⁰ center) are not in general unique. This can be understood in terms of convexity of the associated functions (coercive functions).

The 2-norm and ?-norm are strictly convex, and thus (by convex optimization) the minimizer is unique (if it exists), and exists for bounded distributions. Thus