• Corpus ID: 119684328

Good measures on locally compact Cantor sets

@article{Karpel2012GoodMO,
  title={Good measures on locally compact Cantor sets},
  author={O. Karpel},
  journal={arXiv: Dynamical Systems},
  year={2012}
}
  • O. Karpel
  • Published 30 March 2012
  • Mathematics
  • arXiv: Dynamical Systems
We study the set M(X) of full non-atomic Borel (finite or infinite) measures on a non-compact locally compact Cantor set X. For an infinite measure $\mu$ in M(X), the set $\mathfrak{M}_\mu = \{x \in X : {for any compact open set} U \ni x {we have} \mu(U) = \infty \}$ is called defective. We call $\mu$ non-defective if $\mu(\mathfrak{M}_\mu) = 0$. The class $M^0(X) \subset M(X)$ consists of probability measures and infinite non-defective measures. We classify measures $\mu$ from $M^0(X)$ with… 
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References

SHOWING 1-10 OF 16 REFERENCES
Infinite measures on Cantor spaces
We study the set of all infinite full non-atomic Borel measures on a Cantor space X. For a measure from , we define a defective set . We call a measure from non-defective ( ) if . The paper is
Homeomorphic measures on stationary Bratteli diagrams
We study the set S of ergodic probability Borel measures on stationary non-simple Bratteli diagrams which are invariant with respect to the tail equivalence relation. Equivalently, the set S is
Good measures on Cantor space
While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically
On homeomorphic Bernoulli measures on the Cantor space
Let be the Bernoulli measure on the Cantor space given as the infinite product of two-point measures with weights and . It is a long-standing open problem to characterize those and such that and are
A pair of non-homeomorphic product measures on the Cantor set
  • Tim Austin
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2007
Abstract For r ∈ [0, 1] let μ r be the Bernoulli measure on the Cantor set given as the infinite power of the measure on {0, 1} with weights r and 1 − r. For r, s ∈ [0, 1] it is known that the
Typical Dynamics of Volume Preserving Homeomorphisms
Historical Preface General outline Part I. Volume Preserving Homomorphisms of the Cube: 1. Introduction to Parts I and II (compact manifolds) 2. Measure preserving homeomorphisms 3. Discrete
STRONG ORBIT EQUIVALENCE OF LOCALLY COMPACT CANTOR MINIMAL SYSTEMS
We study minimal self-homeomorphisms of zero dimensional metrizable locally compact non-compact Hausdorff spaces. For this class of systems, we show that the ordered cohomology group is a complete
(C, F)-Actions in Ergodic Theory
This is a survey of a recent progress related to the (C, F)-construction of funny rank-one actions for locally compact groups. We exhibit a variety of examples and counterexamples produced via the
WEAK ORBIT EQUIVALENCE OF CANTOR MINIMAL SYSTEMS
This paper is a commentary on the recent work [4]. It has two goals: the first is to eliminate the C*-algebra machinery from the proofs of the results of [4]; the second, to provide a
Invariant measures on stationary Bratteli diagrams
Abstract We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we give an explicit description of all ergodic probability measures that
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