Non-Uniform Estimates and Asymptotic Expansions of the Remainder in the Central Limit Theorem for m-Dependent Random Variables

We study the order structure induced on a rigged Hilbert space ?? ? χ ? ??′by a self-dual cone in χ. Under the assumption that ?? is a semi-reflexive locally convex vector lattice, and a solid subset of ??′ (we speak then of a rigged Hilbert lattice), we show that ??′ is in fact a nondegenerate partial inner product space.