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...



If a Borelian set has positive measure, does it contain a non empty open set  (minus a measure null set)?
The Cantor set of positive measure is nowhere dense set. So it is an example.


