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),pρ,g和pφ,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.
In this paper, we consider equivalent metrics. We prove that the the diameter-type packing measures with respect to diameter-type packing measures Pρ'g and pφ,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.