Journal article
MEASURES ON CANTOR SETS: THE GOOD, THE UGLY, THE BAD
Transactions of the American Mathematical Society, Vol.366(12), pp.6247-6311
12/01/2014
DOI: 10.1090/S0002-9947-2014-06035-2
Abstract
We translate Akin's notion of good (and related concepts) from measures on Cantor sets to traces on dimension groups, and particularly for invariant measures of minimal homeomorphisms (and their corresponding simple dimension groups). This yields characterizations and examples, which translate back to the original context. Good traces on a simple dimension group are characterized by their kernel having dense image in their annihilating set of affine functions on the trace space; this makes it possible to construct many examples with seemingly paradoxical properties.
In order to study the related property of refinability, we consider goodness for sets of measures (traces on dimension groups), and obtain partial characterizations in terms of (special) convex subsets of Choquet simplices.
These notions are also very closely related to unperforation of quotients of dimension groups by convex subgroups (that are not order ideals), and we give partial characterizations. Numerous examples illustrate the results.
Details
- Title: Subtitle
- MEASURES ON CANTOR SETS: THE GOOD, THE UGLY, THE BAD
- Creators
- Sergey Bezuglyi - Institute for Low Temperature Physics, 47 Lenin Avenue, 61103 Kharkov, UkraineDavid Handelman - University of Ottawa
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.366(12), pp.6247-6311
- DOI
- 10.1090/S0002-9947-2014-06035-2
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Publisher
- American Mathematical Society
- Number of pages
- 65
- Grant note
- NSERC; Natural Sciences and Engineering Research Council of Canada (NSERC)
- Language
- English
- Date published
- 12/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984240764902771
Metrics
26 Record Views