  We present a self-contained and modern survey of some existing quasi-sure
results via the connection to the Brownian sheet. Among other things, we prove
that quasi-every continuous function: (i) satisfies the local law of the
iterated logarithm; (ii) has Levy's modulus of continuity for Brownian motion;
(iii) is nowhere differentiable; and (iv) has a nontrivial quadratic variation.
We also present a hint of how to extend (iii) to obtain a quasi-sure refinement
of the M. Csorgo--P. Revesz modulus of continuity for almost every continuous
function along the lines suggested by M. Fukushima.
