Vol. 33, No. 1, 1970

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A generalized Hausdorff dimension for functions and sets

Robert Jay Buck

Vol. 33 (1970), No. 1, 69–78

A generalization of the Hausdorff dimension of sets is given by restricting the lengths of the intervals in the covering family. The dependence of this dimension on the choice of covering family is studied by considering the set of points in the countable unit cube Iω whose coordinates are the values of the dimensions of some set for a fixed, countable collection of covering families. General conditions are given in order that two families yield the same dimension on each set, and that a covering family give the ordinary Hausdorff dimension.

Mathematical Subject Classification
Primary: 28.13
Received: 3 January 1969
Published: 1 April 1970
Robert Jay Buck