Let $B(t)$ denote Brownian motion in $R^d$. It is a classical fact that for any Borel set $A$ in $R^d$, the volume $V_1(A)$ of the Wiener sausage $B[0,1]+A$ has nonzero expectation iff $A$ is nonpolar. We show that for any…

We provide a simple probabilistic proof of a result of J. Král and I. Netuka: If  $f$ is a measurable real-valued function on $\mathbb{R}^d$ ($d > 1$) then the set of points at which  $f$ has a strict fine local…