I want to show that the Borel sigma-algebra over $\mathbb R^n$ can be generated by A, the set of closed sets of $\mathbb R^n$, i.e. $A = \{C \subset \mathbb R^n$ : C is closed$\}$.
I could show that this statement holds true in $\mathbb R$. Is there a theorem or something like that which I can use to deduce that if the statement is true in $\mathbb R$, it's also true in $\mathbb R^n$?