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Introduced in 1946 by P.A.P Moran,<ref>Moran, P.A.P. (1946) Additive Functions of Intervals and Hausdorff Measure. Proceedings-Cambridge Philosophical Society, 42, 15-23.
https://doi.org/10.1017/S0305004100022684</ref> the open set condition is used to compute the dimensions of certain self-similar fractals, notably the Sierpinski Gasket. It is also used to simplify computation of the packing measure.<ref>https://eprints.ucm.es/id/eprint/58898/1/version%20final(previa%20prueba%20imprenta).pdf</ref>
An equivalent statement of the open set condition is to require that the s-dimensional [[Hausdorff measure]] of the set is greater than zero.<ref>https://www.math.cuhk.edu.hk/conference/afrt2012/slides/Wen_Zhiying.pdf</ref>
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