“…By definition, u m (x, λ) is a weighted average of values of u in A m = [x, x + 1/m] × [λ, λ + 1/m]; (a), (b) and (d) follow by standard techniques, because u m ≥ u and u is absolutely continuous in (0, ∞) × (λ, ∞) and satisfies the growth condition (13) (see for instance [30]). From Equation (11) we have that u x ≥ 1 a.e., also since for all (x, λ) ∈ D, L(u) (x, λ) ≤ 0 we have…”