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Journal of the London Mathematical Society 1997 56(3):557-566; doi:10.1112/S0024610798005791
© 1997 by London Mathematical Society
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© The London Mathematical Society

Concerning the Problem of Subsets of Finite Positive Packing Measure

H. Joyce

Department of Mathematics, University of Jyväskylä PL-35 Jyväskylä 10 40351, Finland

Received 21 March 1995. Revision received 13 November 1995.

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.


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