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Non-σ-finite sets for packing measure

Published online by Cambridge University Press:  26 February 2010

H. Haase
Affiliation:
Sektion Mathematik, Ernst-Moritz-Arndt Universität, DDR-2200 Greifswald, F.-L. Jahn Str. 15a.
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Extract

In a recent paper Taylor and Tricot [10] introduced packing measures in ℝd. We modify their definition slightly to extend it to a general metric space. Our main concern is to show that in any complete separable metric space every analytic set of non-σ-finite h-packing measure contains disjoint compact subsets each of non-σ-finite measure. The corresponding problem for Hausdorff measures is discussed, but not completely resolved, in Rogers' book [7]. We also show that packing measure cannot be attained by taking the Hausdorff measure with respect to a different increasing function using another metric which generates the same topology. This means that the class of pacing measures is distinct from the class of Hausdorff measures.

Type
Research Article
Copyright
Copyright © University College London 1986

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