Absolute continuity of stable seminorms (Q1081178)

The authors prove the following Theorem: Let \(\mu\) be a symmetric p- stable measure on a complete separable metric vector space E and let \(q: E\to R^+\) be a lower semicontinuous seminorm. Then the distribution function of q is absolutely continuous, except possibly at \(u_ 0=\inf \{u>0:\) \(F(u)>0\}\). If, additionally either \(0<p<1\), or q is strictly convex, then the distribution of q is either absolutely continuous, or degenerated at 0.