High Quality Content by WIKIPEDIA articles! In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple "diameter to the dimension" power law used in the construction of s-dimensional Hausdorff measure. The idea of a dimension function is to use different functions of diameter than just diam(C)s for some s, and to look for the same property of the Hausdorff measure being finite and non-zero.

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