Let T and R be measure preserving, T weakly mixing, R ergodic, and let S be conservative ergodic and nonsingular. Let T be a weakly mixing compact abelian group extension of T. UTxS is ergodic then T x S is ergodic. A corollary is a new proof that if T is mildly mixing then so is T. A similar statement holds for other ergodic multiplier properties. Now let T be a weakly mixing type a compact af...

Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem j−1

Let Γ be a lattice in G = SL(n,R) and X = G/S a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish uniform distribution of orbits of Γ in X analogous to the classical equidistribution on torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of Borel subgroup ...

We show that there exists a C∞ volume preserving diffeomorphism P of a compact smooth Riemannian manifold M of dimension 4, which is close to the identity map and has nonzero Lyapunov exponents on an open and dense subset G of not full measure and has zero Lyapunov exponent on the complement of G. Moreover, P |G has countably many disjoint open ergodic components.

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...

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say Sn = g X1 + · · · + g Xn , where E g X1 =0 and E g X1 2 <∞. The conditions imposed restrict the moments of g and the growth of the conditional means E Sn X1 . No other restrictions on the dependence structure of the chain are required. When specialized to shift proces...

If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...

Consider a subshift over finite alphabet, $X\subset \Lambda^\mathbb{Z}$ (or $X\subset\Lambda^{\mathbb{N}\_0}$). With each block $B\in\Lambda^k$ appearing in $X$ we associate the empirical measure ascribing to every $C\in\Lambda^l$ frequency of occurrences $C$ $B$. By comparing values ascribed blocks define metric on combined space $B$ and probability measures $\mu$ $X$, whose restriction is com...

Let iX, 03, m) be a finite measure space. We shall denote by L*im) (1 èp< °°) the Banach space of all real-valued (B-measurable functions/ defined on X such that |/[ p is m-integrable, and by L°°(w) the Banach space of all real-valued, (B-measurable, w-essentially bounded functions defined on X; as usual, the norm in Lpim) is given by 11/11,.= {fx\fix)\pdm}1'*, and the norm in Lxim) by \\g\\x =...