“…Here, we consider the general case of u c j = c j ω K j with c j > 0 and K j non-pluripolar, compact, polynomially convex subsets of a bounded hyperconvex domain Ω of C n . In this situation, the functions u c j (z) = −c j precisely on K j and are continuous on Ω, the geodesics u t converge to u j , uniformly on Ω, as t → j, and belong to C(Ω × [0, 1]), as in the non-weighted case dealt with in [18] and [8].…”