Support and Seminorm Integrability Theorems for r-Semistable Probability Measures on LCTVS.
Abstract
Let mu be an r-semistable k-regular probability measure of index a epsilon (0,2) on a complete locally convex topological vector space E. It is shown that the topological support S sub mu of mu is a translated convex cone if alpha epsilon (0, 1), and a translated truncated cone if alpha epsilon (1, 2). Further, if alpha = 1 and mu is symmetric, then it is shown that S sub mu is a vector subspace of E. These results subsume all earlier known results regarding the support of stable measures. Results dealing with the support of infinitely divisible and the seminorm integrability for gamma-semistable measures are also obtained. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1979
- Accession Number
- ADA088342
Entities
People
- Balram S. Rajput
- Donald Louie
Organizations
- University of Tennessee