Let \(\left(B_{t}ight)_{t \geqslant 0}\) be a \(\mathrm{BM}^{1}\) and \(f \in L^{2}\left(\lambda_{T} \otimes \mathbb{P}ight.\) ) for some \(T>0\). Assume that the limit \(\lim _{\epsilon ightarrow 0} f(\epsilon)=f(0)\) exists in \(L^{2}(\mathbb{P})\). Show that \[\frac{1}{B_{\epsilon}} \int_{0}^{\epsilon} f(s) d B_{s} \xrightarrow[\epsilon ightarrow 0]{\mathbb{P}} f(0)\]