Stable elliptically contoured measures in Hilbert space: Asymptotic properties of conditional distributions (Q2763007)

The paper is devoted to the study of conditional distributions generated by the finite-dimensional projections of the \(\sigma\)-additive stable elliptically contoured measure, determined on the real Hilbert space. In the case when the projection dimension tends to infinity the almost sure convergence of conditional distributions to the Gaussian ones is proved. For some scheme of series of families of conditional distributions the strong law of large numbers is stated.