A note on $σ$-point and nontangential convergence

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 $σ$-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 $σ$-points of the measure. We also investigate the relationship between $σ$-point and the notion of the strong derivative introduced by Ramey and Ullrich. In one dimension, these two notions are the same.

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