The packing measure and symmetric derivation basis measure (Q1189106)

Let \(h\) be a continuous, increasing function defined on \(R\) such that \(f(0)=0\) and \(\delta: R^ n\to(0,\infty)\). Then for any \(E\subset R^ n\) it is defined \(H_ s(E)=\sup\{\sum_ i h(2r_ i)\mid (B(x_ i,r_ i))_ i\) is a sequence of pairwise disjoint balls in \(R^ n\), \(x_ i\in E\) and \(0<r_ i<\delta(x_ i)\}\) and \(h_ s(E)=\inf\{H_{s,\delta}(E)\mid \delta: R^ n\to(0,\infty)\}\). The author asserts that \(h_ s(E)=h_{s^*}(E)\), where \(h_{s^*}(E)=\inf\{H_{s,\delta}(E)\mid \delta: R^ n\to(0,\infty)\) is a function of the Baire class three\}.