1. ## a question about the borel set

Is there a borel set A in R2 such that
{x,x belongs to R1 and there is y such that (x,y) belongs to A} is not a borel set in R1.

3. ## Re: a question about the borel set

I red too fast the question, indeed the answer is yes (I red the question as "Is it true that the projection of every Borel set of $\mathbb{R}^2$ is a Borel set of $\mathbb{R}$?").