If a Borelian set has positive measure, does it contain a non empty open set (minus a measure null set)? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T06:59:58Z http://mathoverflow.net/feeds/question/20512 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/20512/if-a-borelian-set-has-positive-measure-does-it-contain-a-non-empty-open-set-mi If a Borelian set has positive measure, does it contain a non empty open set (minus a measure null set)? Nicolò 2010-04-06T15:28:14Z 2010-04-06T15:35:05Z <p>Let A be a borelian set with postivie measure. I was asking myself if it is possible to find an open set \$B\subseteq A\$ such that \$B\$ is an open set minus a set of null measure...</p> http://mathoverflow.net/questions/20512/if-a-borelian-set-has-positive-measure-does-it-contain-a-non-empty-open-set-mi/20513#20513 Answer by Petya for If a Borelian set has positive measure, does it contain a non empty open set (minus a measure null set)? Petya 2010-04-06T15:35:05Z 2010-04-06T15:35:05Z <p>The Cantor set of positive measure is nowhere dense set. So it is an example.</p>