Research Article

Non-σ-finite sets for packing measure

H. Haasea1

a1 Sektion Mathematik, Ernst-Moritz-Arndt Universität, DDR-2200 Greifswald, F.-L. Jahn Str. 15a.

In a recent paper Taylor and Tricot [10] introduced packing measures in d. 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.

(Received September 11 1985)

Key Words:

  • 28A12: MEASURE AND INTEGRATION; Classical measure theory; Contents, measures, outer measures, capacities.