# Question on whether a set is measurable

Let $A$ be a non-Lebesgue measurable set, and let $B=[0,1]\subseteq\mathbb{R}$. Show that $C=A\times B$ is non-measurable.

I try use the regularity of the lebesgue measure, but don´t work, maybe take a set of borel sets and suppose $C$ is measurable give something..

Thanks.

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You might use this result. If $C\subseteq [0,1]^2$ is product Borel measurable, then the section sets $$A_x = \{s\in [0,1]| (x,s)\in C\}$$ are measurable.
If $C$ is product Lebesgue mesurable, then the $A_x$ are measurable almost everywhere.