User:IntegralPython/sandbox/Fractal measure: Difference between revisions

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m IntegralPython moved page Draft:Fractal measure to User:IntegralPython/sandbox/Fractal measure: Not focused enough to be an article: I'm going to try to shift focus myself since I'm the only active watcher of the article
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'''Fractal measure''' is any [[measure (mathematics)|measure]] which generalizes the notions of length, area, and [[volume]] to non-[[integer]] dimensions, especially in application towards [[fractal]]s. There is no unique fractal measure, in part although not entirely due to the lack of a unique definition of [[fractal dimension]]; the most common fractal measures include the [[Hausdorff measure]] and the packing measure, based off of the [[Hausdorff dimension]] and [[packing dimension]] respectively.<ref>http://www.diva-portal.org/smash/get/diva2:22333/FULLTEXT01</ref> Fractal measures are measures in the sense of [[measure theory]], and are usually defined to agree with the ''n''-dimensional [[Lebesgue measure]] when ''n'' is an integer.<ref>https://link.springer.com/chapter/10.1007/978-1-4757-2958-0_1</ref> Fractal measure can be used to define the fractal dimension or vice versa. Although related, differing fractal measures are not equivalent, and may provide different measurements for the same shape.