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Generalized Hausdorff measure for generic compact sets
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Balka, Richárd and Máthé, András (2013) Generalized Hausdorff measure for generic compact sets. Annales Academiae Scientiarum Fennicae Mathematica , Volume 38 (Number 2). pp. 797-804. doi:10.5186/aasfm.2013.3835 ISSN 1239-629X.
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Official URL: http://dx.doi.org/10.5186/aasfm.2013.3835
Abstract
Let X be a Polish space. We prove that the generic compact set K subset of X (in the sense of Baire category) is either finite or there is a continuous gauge function h such that 0 < H-h(K) < infinity, where H-h denotes the h-Hausdorff measure. This answers a question of Cabrelli, Darji, and Molter. Moreover, for every weak contraction f : K --> X we have H-h (K boolean AND f (K)) = 0. This is a measure theoretic analogue of a result of Elekes.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Annales Academiae Scientiarum Fennicae Mathematica | ||||||||
Publisher: | Suomalainen Tiedeakatemia | ||||||||
ISSN: | 1239-629X | ||||||||
Official Date: | 2013 | ||||||||
Dates: |
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Volume: | Volume 38 | ||||||||
Number: | Number 2 | ||||||||
Page Range: | pp. 797-804 | ||||||||
DOI: | 10.5186/aasfm.2013.3835 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) |
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