A Certain Regular Property of the Method I Construction and Packing Measure

✍ Scribed by Sheng You Wen

• Publisher: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• Year: 2007
• Tongue: English
• Weight: 156 KB
• Volume: 23
• Category: Article
• ISSN: 1439-7617
• DOI: 10.1007/s10114-007-0955-3

✦ Synopsis

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.