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We give a very simple and elementary proof of the existence of a weaklycompact family of probability measures $\{P_{\theta}:\theta \in \Theta \}$ torepresent an important sublinear expectation--G-expectation$\mathbb{E}[\cdot]$. We also give a concrete approximation of a boundedcontinuous function $X(\omega)$ by an increasing sequence of cylinder functions$L_{ip}(\Omega)$ in order to prove that $C_{b}(\Omega)$ belongs to the$\mathbb{E}[|\cdot|]$-completion of the $L_{ip}(\Omega)$.

On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion