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Let $f\left(x\right)$ be a nonnegative function with its only singularity at $x=0$, e.g. $f\left(x\right)=|x{|}^{-\alpha }$, $\alpha \>0$. We study the behavior of the Wiener process $W\left(t\right)$ in left and right hand neighborhoods of level crossings by finding necessary and sufficient conditions on $f$ for the integrals of $f\left(W\right(t\left)\right)$ to be finite or infinite.