Characterization of multidimensional stable random measures by means of vector measures

In connection with a symmetric a stable random measure 4) on a measurable space (F,F) with values in R-d, a complete metric space. of symmetric finite measures on Sd-1 is constructed, and is employed to characterize the law of (D by a unique positive measure on 9 and a unique function on F x R-d. The stochastic integral integral(F) f dPhi is also defined for certain d x d matrix valued functions f, which for alpha = 2 reduces to the Wiener-Masani integral.