ABSTRACT
We shall prove that the Gauss-Weierstrass integral of a signed measure μ has what is called a ‘parabolic limit’ at almost every point of R̲n × {0}. To do this, we shall use a notion of differentiability of the initial measure μ. We shall then look at the possibility of improving this result by replacing the parabolic approach to the boundary with a less restricted one. It turns out that no simple improvement is possible, but that a slightly better result can be obtained if approach through a complicated region is allowed, at least, in the case where μ is absolutely continuous with respect to Lebesgue measure. To achieve this, an argument involving what are called ‘maximal functions’ is used.
