Editing Smith–Volterra–Cantor set (section)

{{Short description|Set of real numbers in mathematics}}
[[Image:Smith-Volterra set.png|thumb|right|256px|After black intervals have been removed, the white points which remain are a nowhere dense set of measure 1/2.]] 
In [[mathematics]], the '''Smith–Volterra–Cantor set''' ('''SVC'''), '''ε-Cantor set''',<ref>Aliprantis and Burkinshaw (1981), Principles of Real Analysis</ref> or '''fat Cantor set''' is an example of a set of points on the [[real line]] that is [[nowhere dense]] (in particular it contains no [[interval (mathematics)|interval]]s), yet has positive [[measure (mathematics)|measure]]. The Smith–Volterra–Cantor set is named after the [[mathematician]]s [[Henry John Stephen Smith|Henry Smith]], [[Vito Volterra]] and [[Georg Cantor]].  In an 1875 paper, Smith discussed a nowhere-dense set of positive measure on the real line,<ref>[[Henry John Stephen Smith|Smith, Henry J.S.]] (1874). "[https://babel.hathitrust.org/cgi/pt?id=ucm.5324906759;view=1up;seq=148 On the integration of discontinuous functions]". Proceedings of the London Mathematical Society. First series. 6: 140–153
</ref> and Volterra introduced a similar example in 1881.<ref>{{Cite journal |last1=Ponce Campuzano |first1=Juan |last2=Maldonado |first2=Miguel |date=2015 |title=Vito Volterra's construction of a nonconstant function with a bounded, non Riemann integrable derivative |journal=BSHM Bulletin Journal of the British Society for the History of Mathematics |volume=30 |issue=2 |pages=143–152 |doi=10.1080/17498430.2015.1010771|s2cid=34546093 }}</ref>  The Cantor set as we know it today followed in 1883. The Smith–Volterra–Cantor set is [[Homeomorphism|topologically equivalent]] to the [[Cantor set|middle-thirds Cantor set]].