An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

Document Type : Research Paper


1 Kuwait University and Shiraz University

2 Isfahan University of Technology


A consistency criteria is given for a certain class of finite positive
measures on the surfaces of the finite dimensional unit balls in a real
separable Hilbert space. It is proved, through a Kolmogorov type existence
theorem, that the class induces a unique positive measure on the surface of
the unit ball in the Hilbert space. As an application, this will naturally
accomplish the work of Kanter (1973) on the existence and uniqueness of the
spectral measures of finite dimensional stable random vectors to the
infinite dimensional ones. The approach presented here is direct and
different from the functional analysis approach in Kuelbs (1973), Linde
(1983) and the indirect approach of Tortrat (1976) and Dettweiler (1976).


Main Subjects