The idea was a generalisation of one which had been introduced five years earlier by Carathéodory but Hausdorff realised that Carathéodory 's construction made sense, and was useful, for defining fractional dimensions. Hausdorff's paper includes a proof that the dimension of the middle-third Cantor set is log 2/log 3. Chatterji writes:
Ang mga ideya ay isang generalisation ng isa na may ay ipinakilala ng limang taon na mas maaga sa pamamagitan ng Carathéodory ngunit Hausdorff realised na Carathéodory 's construction na ginawa ng kahulugan, at noon ay kapaki-pakinabang, para sa pagtukoy fractional sukat. Hausdorff ng papel kasama ang isang patunay na ang laki ng gitnang-third kantor set ay mag-log 2/log 3. Chatterji magsusulat: