Dilatation monotonicity and convex order
The author shows that a convex, lower semicontinuous function on \(L^p\), \(p\geq1\), is law invariant if and only if it is monotonic with respect to convex order and if and only if it is dilatation monotonic. Moreover, dropping the assumption of convexity, for any lower semicontinuous function, dilatation monotonicity is equivalent to order monotonicity with respect to convex order.
scientific article; zbMATH DE number 6366179