Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
Properness of preferences are useful for proving existences of an equilibrium and of supporting prices in Banach Lattices. In this paper we characterize completely properness and uniform properness for separable concave functions defined in $L^{p}_{+}.$ We prove also that every separable concave function which is well-defined in $L^{p}$ is automatically continuous.