On hardly visited points of the Brownian motion (Q1187101)

Let \(L(xt)\) be the local time process of a standard Wiener process \(\{W(t),\;t>0\}\). Denote \[ T_ r=\inf\{t>0;\;L(0,t)\geq r\}, \qquad \mu(r,q)=\mu(y;\;0<L(y,T_ r)<q). \] The almost sure behavior of the random measure \(\mu(r,q)\) is investigated.