• Corpus ID: 119684328

Good measures on locally compact Cantor sets

  title={Good measures on locally compact Cantor sets},
  author={O. Karpel},
  journal={arXiv: Dynamical Systems},
  • 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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