Maharam Extension for Nonsingular Group Actions
نویسندگان
چکیده
منابع مشابه
Maharam extension and stationary stable processes
We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences. 1. Introduction. In a fundamental paper [9], Rosi´nski revealed the hidden structure of stationary symmetric α-stable (SαS) processes. Namely, he proved t...
متن کاملWeak Mixing Properties for Nonsingular Actions
For a general group G we consider various weak mixing properties of nonsingular actions. In the case where the action is actually measure preserving all these properties coincide, and our purpose here is to check which implications persist in the nonsingular case.
متن کاملThe C Closing Lemma for Nonsingular Endomorphisms Equivariant under Free Actions of Finite Groups
In this paper a closing lemma for C1 nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C1 equivariant perturbation.
متن کاملProperty (T) and the Furstenberg Entropy of Nonsingular Actions
We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure μ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg μ-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condit...
متن کاملCharacterizing Mildly Mixing Actions by Orbit Equivalence of Products
We characterize mildly mixing group actions of a noncompact locally compact second countable group G using orbit equivalence We show an amenable action of G is mildly mixing if and only if G is amenable and for any nonsingular ergodic G action the product G action is orbit equivalent to We extend the result to the case of nite measure preserving noninvertible endomorphisms i e when G N and show...
متن کامل