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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.