# Can anyone give me an example of a measurable subset of the interval [10,100], that is not a Borel set.

I know how to construct a measurable set of a Cantor set that is not Borel but the example will be of the form $f^{-1}(E)$ is a subset of cantor set and is measurable (where $f$ is homeomorphism from Cantor set to a set of positive outer measure). So I would like an example of a measurable subset of the interval (say [10,100]), that is not a Borel set.

• Without Axiom of Choice? – Przemysław Scherwentke Feb 12 '18 at 18:19
• – Jack D'Aurizio Feb 12 '18 at 18:19
• Why not scale and translate the set you already have? – Xander Henderson Feb 12 '18 at 18:19