Abstract
Let τ be a premeasure on a complete separable metric space and let τ* be the Method I measure constructed from τ. We give conditions on τ such that τ* has a regularity as follows: Every τ*-measurable set has measure equivalent to the supremum of premeasures of its compact subsets. Then we prove that the packing measure has this regularity if and only if the corresponding packing premeasure is locally finite.
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Supported by the Natural Science Foundation of China (10571063). The work is partly carried out in the Morningside Center of Mathematics, Chinese Academy of Sciences
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Wen, S.Y. A Certain Regular Property of the Method I Construction and Packing Measure. Acta Math Sinica 23, 1769–1776 (2007). https://doi.org/10.1007/s10114-007-0955-3
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DOI: https://doi.org/10.1007/s10114-007-0955-3