Let \(D\subset {\mathbb{C}}^ n\) (n\(\geq 2)\) be a domain with \(C^ 2\)- boundary. We say that a function \(f\in {\mathcal O}(D)\) is normal if there exists a constant M such that \({\mathcal L}_{\log (1+| f|^ 2)}(z;v)\leq M\kappa_ D(z;v)\), \(z\in D\), \(v\in {\mathbb{C}}^ n\), where \({\mathcal L}\) denotes the Levi form and \(\kappa_ D\) is the Kobayashi- Royden metric for D. For \(\xi\in \partial D\) and \(\alpha >0\) let \[ D_{\alpha}(\xi):=\{z\in D: | | 0\) then for any \(\alpha\lim_{D_{\alpha}(\xi)\ni z\to \xi}f(z)=a.\) Moreover, he shows that if D is strongly pseudoconvex and if f is a normal function such that \(\int_{D}[| \nabla_ Df(z)|^ 2/(1+| f(z)|^ 2)]d\Omega (z)<+\infty,\) where \(| \nabla_ Df(z)|\) and \(d\Omega\) (z) are taken in sense of the Bergman metric, then for almost all \(\xi\in \partial D\) the limit \(\lim_{D_{\alpha}(\xi)\ni z\to \xi}f(z)\) exists.