Derivation bases and the Hausdorff measure (Q1101560)

The author deals with a problem posed by \textit{B. S. Thomson} [Real Anal. Exch. 8, 67-207 (1983; Zbl 0525.26002)]. Some sufficient conditions are shown such that the Hausdorff measure on a set equals to the measure generated by the usual derivation basis. It is also shown that the symmetric derivation basis gives rise to a measure which is finite on more sets of finite Hausdorff measure than the measure from the usual derivation basis.