'''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 [[hausdorffHausdorff measure]] and the packing measure, based off of the [[hausdorffHausdorff 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 measures find application in the study of fractal geometry, as well as in [[physics]] and [[biology]] through the study of [[fractal derivative]]s.<ref>{{cite journal |first=W. |last=Chen |title=Time–space fabric underlying anomalous diffusion |journal=Chaos, Solitons and Fractals |volume=28 |issue= 4|pages=923–929 |year=2006 |doi= 10.1016/j.chaos.2005.08.199|url=|arxiv=math-ph/0505023 |bibcode=2006CSF....28..923C |s2cid=18369880 }}</ref> Fractal measure can be used to define the fractal dimension or vice versa.
Although related, differing fractal measures are not the same, and may provide different measurements for the same shape.
