How from the Law of the Iterated Logarithm for the Brownian Motion
For a standard Brownian motion $B$, we have $P(\limsup_{t->0^+} \frac{B_t}{\sqrt{2t\log \log t^{-1}}}=1)=1$
do we get the following? $h(t)=\sqrt{2t\log \log t^{-1}}$
I get that $\limsup A_n$ is equivalent to $A_n$ i.o., but this relation is just for a sequence of sets, not a sequence of real numbers...