数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2007年
2期
153-156
,共4页
直径型填充测度%纲函数%加倍条件%等价
直徑型填充測度%綱函數%加倍條件%等價
직경형전충측도%강함수%가배조건%등개
diameter-type packing measure%gauge function%doubling condition%equivalence
本文研究了在等价度量下,直径型填充测度之间的关系,证明了对任意紧度量空间(X,ρ),P(ρ,g)和P(cρ,g)等价当且仅当纲函数g满足加倍条件.所得结论揭示了填充测度与加倍条件之间的关系.
本文研究瞭在等價度量下,直徑型填充測度之間的關繫,證明瞭對任意緊度量空間(X,ρ),P(ρ,g)和P(cρ,g)等價噹且僅噹綱函數g滿足加倍條件.所得結論揭示瞭填充測度與加倍條件之間的關繫.
본문연구료재등개도량하,직경형전충측도지간적관계,증명료대임의긴도량공간(X,ρ),P(ρ,g)화P(cρ,g)등개당차부당강함수g만족가배조건.소득결론게시료전충측도여가배조건지간적관계.
In this paper,we consider the diameter-type packing measures with respect to equivalent metrics.We prove that the diameter-type packing measures P(ρ,g) and P(cρ,g) are equivalent for any compact metric space(X,ρ) if and only if the gauge function g satisfies the doubling condition.The results reveal the relation between packing measure and doubling condition.
