Resumen de Poly-adic filtrations, standardness, complementability and maximality
Given some essentially separable filtration (Zn)n≤0(Zn)n≤0 indexed by the nonpositive integers, we define the notion of complementability for the filtrations contained in (Zn)n≤0(Zn)n≤0. We also define and characterize the notion of maximality for the poly-adic sub-filtrations of (Zn)n≤0(Zn)n≤0. We show that any poly-adic sub-filtration of (Zn)n≤0(Zn)n≤0 which can be complemented by a Kolmogorovian filtration is maximal in (Zn)n≤0(Zn)n≤0. We show that the converse is false, and we prove a partial converse, which generalizes Vershik’s lacunary isomorphism theorem for poly-adic filtrations.
