in this paper, a local approach to the concept of hudetz $g$-entropy is presented. the introduced concept is stated in terms of hudetz $g$-entropy. this representation is based on the concept of $g$-ergodic decomposition which is a result of the choquet's representation theorem for compact convex metrizable subsets of locally convex spaces.

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

In this paper we study the problems of invariant and ergodic expectations under G-expectation framework. In particular, the stochastic differential equations driven by G-Brownian motion (G-SDEs) have the unique invariant and ergodic expectations. Moreover, the invariant and ergodic expectations of G-SDEs are also sublinear expectations. However, the invariant expectations may not coincide with ...

We show that for any co-amenable compact quantum group A = C(G) there exists a unique compact Hausdorff topology on the set EA(G) of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G over a locally compact Hausdorff space T the map T → EA(G) sending each t in T to the isomorphism class of the fibre at t is continuous if a...

Let D be a uniform discrete subgroup of a simply connected, connected nilpotent Lie group (i.e. N D N D ... DN D N = e,N = [N,N*] andN/Dis compact). There is a unique normalised "Haar" measure m on N/D which is preserved by left translations. Let A ; N -> N, AD C D be an automorphism and let a E N. Then T(xD) = aAxD is called an affine transformation of the nilmanifold N/D. If etEN is a one-par...

Theorem. Suppose that G is a connected group locally isomorphic to a product of copies of SU(2) and U(1). If n > 2, then the Out(Fn)-action on Hom(Fn, G)/G is ergodic. We conjecture that Out(Fn) is ergodic on each connected component of Hom(Fn, G)/G for every compact Lie group G and n > 2. When G = U(1), then this action is just the action of GL(n,Z) on the n-torus R/Z, which is well known to b...

Let G be a locally compact group and μ measure on G. In this paper we find conditions for the convolution operators λp(μ):Lp(G)→Lp(G) to mean ergodic uniformly ergodic. The properties of λp(μ) are related as well.

We prove that if G is a countable discrete group with property (T) over an infinite subgroup H < G which contains an infinite Abelian subgroup or is normal, then G has continuum many orbit inequivalent measure preserving a.e. free ergodic actions on a standard Borel probability space. Further, we obtain that the measure preserving a.e. free ergodic actions of such a G cannot be classified up to...

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.