# 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} }

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…

## 2 Citations

Bratteli diagrams: structure, measures, dynamics

- Mathematics
- 2015

This paper is a survey on general (simple and non-simple) Bratteli diagrams which focuses on the following topics: finite and infinite tail invariant measures on the path space $X_B$ of a Bratteli…

## References

SHOWING 1-10 OF 16 REFERENCES

Infinite measures on Cantor spaces

- Mathematics
- 2011

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

- Mathematics
- 2010

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

- Mathematics
- 2004

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

- Mathematics
- 2007

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

- MathematicsMathematical 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

- Mathematics
- 2001

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

- Mathematics
- 2001

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

- Mathematics
- 2007

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

- Mathematics
- 1995

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

- MathematicsErgodic Theory and Dynamical Systems
- 2009

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…