Polar point for planar Brownian motion
= Polar point for planar Brownian motion
{title2=$\mathbb P_z(T_w<\infty)=0\quad(z\ne w)$}
A prescribed point is almost surely never visited by <planar Brownian motion> started elsewhere. The <harmonic function> $\log|z-w|$ gives an annular hitting probability that tends to zero as the inner radius decreases to zero. This does not contradict <recurrence of planar Brownian motion>, which concerns neighbourhoods.