Let $A$ be a (bounded) Borel set in $R^n$. Then we know that its projection $A\_1$ on $R^{n-1}$ does not have to be Borel. But does $A\_1$ have the following property?



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> Let $\mu$ be a given nonnegative, finite Borel measure on $R^{n-1}$. Then:
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> $\forall\epsilon>0 \ \exists B,C\subset R^{n-1}$ Borel sets, such that $B\subset A\_1\subset C$ and $\mu(C\setminus B)<\epsilon$.
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Another question on Borel sets and projections
Yes. Projections of Borel sets are analytic sets, and these are measurable with respect to completions of Borel measures. (In fact, it will be possible to get $\mu(C\setminus B)=0$.)


