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 devoted to the classification of measures from with respect to a homeomorphism. The notions of goodness and clopen values set are defined for a non-defective measure . We give a criterion when two good non-defective measures are homeomorphic and prove that there exist continuum classes of weakly homeomorphic good non-defective measures on a Cantor space. For any group-like subset , we find a good non-defective measure on a Cantor space X with and an aperiodic homeomorphism of X which preserves . The set S of infinite ergodic ℛ-invariant measures on non-simple stationary Bratteli diagrams consists of non-defective measures. For the set is group-like, a criterion of goodness is proved for such measures. We show that a homeomorphism class of a good measure from S contains countably many distinct good measures from . [ABSTRACT FROM AUTHOR]

Copyright of Journal of Difference Equations & Applications is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)