2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228886We give a very simple and elementary proof of the existence of a weakly compact family of probability measures $\{P_θ:θ\in Θ\}$ to represent an important sublinear expectation--G-expectation $\mathbb{E}[\cdot]$. We also give a concrete approximation of a bounded continuous function $X(ω)$ by an increasing sequence of cylinder functions $L_{ip}(Ω)$ in order to prove that $C_{b}(Ω)$ belongs to the $\mathbb{E}[|\cdot|]$-completion of the $L_{ip}(Ω)$.12 pagesProbability60H10, 60H05, 60H30, 60E05, 60E07, 62C05, 62D05text