New Proofs that Weak Mixing is Generic.
Nombres normaux
Nous rassemblons divers résultats sur les nombres normaux et en déduisons de nouveaux résultats.
Non-abelian extensions have nonsimple spectrum
Noncommutative Poincaré recurrence theorem
Poincaré’s classical recurrence theorem is generalised to the noncommutative setup where a measure space with a measure-preserving transformation is replaced by a von Neumann algebra with a weight and a Jordan morphism leaving the weight invariant. This is done by a suitable reformulation of the theorem in the language of -space rather than the original measure space, thus allowing the replacement of the commutative von Neumann algebra by a noncommutative one.
Note on weakly mixing transformations.
Note on weakly mixing transformations. (Summary).
Number theoretic expansions, algorithms and metrical observations.
On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.
On a function that realizes the maximal spectral type
We show that for a unitary operator U on , where X is a compact manifold of class , , and μ is a finite Borel measure on X, there exists a function that realizes the maximal spectral type of U.
On a Gauss-Kuzmin type problem for piecewise fractional linear maps with explicit invariant measure.
On a local ergodic theorem
On a nonstandard approach to invariant measures for Markov operators
We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.
On A Paper Of Saha And Ray
On a pointwise ergodic theorem for multiparameter semigroups.
Let Ti (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ Lp(μ) the averagesAnf(x) = (n + 1)-d Σ0≤ni≤n f(T1n1T2n2 ... Tdnd x)converge a.e. on X if and only if there exists a finite invariant measure ν (under the transformations Ti) absolutely continuous with respect to μ and a sequence {XN} of invariant sets with XN ↑ X such that νB > 0 for all nonnull invariant sets B and...
On a problem of R. C. Baker
On a ratio ergodic theorem
On a relationship between the integrabilities of various maximal functions.
On a series of cosecants related to a problem in ergodic theory
On Borel Automorphisms and Their Quasi-Invariant Measures.
On disjointness properties of some smooth flows
Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange...