High Quality Content by WIKIPEDIA articles! In mathematics, a pre-measure is a function that is, in some sense, a precursor to a bona fide measure on a given space. Pre-measures are particularly useful in fractal geometry and dimension theory, where they can be used to define measures such as Hausdorff measure and packing measure on (subsets of) metric spaces. In mathematics, more specifically in measure theory, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, volume, et cetera. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area and volume of Euclidean geometry to suitable subsets of Rn, n = 1, 2, 3, ....

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