The convex conjugate of a polyhedral convex function ( a convex function with polyhedral epigraph ) is again a polyhedral convex function .
The convex conjugate of a closed convex function is again a closed convex function .
The convex function of a polyhedral convex function ( a convex function with polyhedral epigraph ) is again a polyhedral convex function .
The convex conjugate of a closed convex function is again a closed convex function .