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CONCERNING THE PROBLEM OF SUBSETS OF FINITE POSITIVE PACKING MEASURE

Published online by Cambridge University Press:  01 December 1997

H. JOYCE
H. JOYCE
Affiliation:
Department of Mathematics, University of Jyväskylä, PL-35 Jyväskylä10 40351, Finland
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Abstract

For every Hausdorff function h, the paper gives a construction of a compact metric space of infinite diameter-based h-packing measure which has no subsets of positive finite measure. It then indicates how such a construction can be modified to provide the same result for a radius-based packing measure in the case of certain Hausdorff functions which do not satisfy a doubling condition. This is in surprising contrast to another result which shows that for a particular radius-based definition of packing measure no such example can be found.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 557 - 566
Copyright
The London Mathematical Society 1997

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