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    Hausdorff Measure

    Definition

    Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every r>0, A can be covered by a countable family of closed sets, each of diameter less than r, such that the sum of the dth powers of their diameters is less than y. Note that H^d(A) may be infinite, and d need not be an integer.

    Associated person

    Felix Hausdorff

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