Some properties of packing measure with doubling gauge
Let g be a doubling gauge. We consider the packing measureP g and the packing premeasureP g in a metric space X. We rst show that ifP g 0 (X) is nite, then as a function of X,P g has a kind of \outer regularity". Then we prove that if X is complete separable, then supP g 0 (F ) P g (B) supP g 0 (F ) for every Borel subset B of X, where the supremum is taken over all compact subsets of B having nite P g -premeasure, and is a positive number depending only on the doubling gauge g. As an application, we show that for every doubling gauge function, there is a compact metric space of nite positive packing measure.