  This case study proposes robustness quantifications of many classical sample
path properties of Brownian motion in terms of the (mean) deviation frequencies
along typical a.s.~approximations. This includes L\'evy's construction of
Brownian motion, the Kolmogorov-Chentsov (and the Kolmogorov-Totoki) continuity
theorem, L\'evy's modulus of continuity, the Paley-Wiener-Zygmund theorem, the
a.s.~approximation of the quadratic variation as well as the laws of the
iterated logarithm by Khinchin, Chung and Strassen, among others.
