The tail behavior of a stable measure with respect to a seminorm is determined. Bounds are obtained for the measure of small spheres. The geometric structure of the support of stable measures with index $p > 1$ is described.
"Stable Measures and Seminorms." Ann. Probab. 3 (5) 865 - 875, October, 1975. https://doi.org/10.1214/aop/1176996273