# Each <math>\psi_i (V)</math> is pairwise disjoint.
Introduced in 1946 by P.A.P Moran,<ref>{{cite journal | last=Moran, | first=P.A.P. (1946)| title=Additive Functions of Intervals and Hausdorff Measure. | journal=Proceedings-Cambridge Philosophical Society, | volume=42, | year=1946 | pages=15-23 | doi=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>{{cite journal| last1=Llorente|first1=Marta|last2=Mera|first2=M. Eugenia| last3=Moran| first3=Manuel| title= On the Packing Measure of the Sierpinski Gasket | journal= University of Madrid | url=https://eprints.ucm.es/id/eprint/58898/1/version%20final(previa%20prueba%20imprenta).pdf}}</ref>
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>
{{cite web |url=https://www.math.cuhk.edu.hk/conference/afrt2012/slides/Wen_Zhiying.pdf |title=Open set condition for self-similar structure |last= Wen |first=Zhi-ying |publisher=Tsinghua University |access-date= 1 February 2022 }} </ref>
