  In this article, we generalize a theorem of Victor L. Shapiro concerning
nontangential convergence of the Poisson integral of a $L^p$-function. We
introduce the notion of $\sigma$-points of a locally finite measure and
consider a wide class of convolution kernels. We show that convolution
integrals of a measure have nontangential limits at $\sigma$-points of the
measure. We also investigate the relationship between $\sigma$-point and the
notion of the strong derivative introduced by Ramey and Ullrich. In one
dimension, these two notions are the same.
