  In this paper, we shall study the basic absolute properties of $G$-Brownian
motion, i.e., those properties which hold for q.s. $\omega$. These include the
characterization of the zero set and the local maxima of the $G$-Brownian
motion paths. We also show that the indicator function of $G$-Brownian motion
is in $\mathbb{L}_G^1(\Omega)$, which is an useful tool for the study of
$G$-expectation theory.
