Borel Sigma-Algebra on Euclidean Space by Monotone Class

Theorem
Let $\left({\R^n, \tau}\right)$ be the $n$-dimensional Euclidean space.

Then $\mathcal B \left({\R^n, \tau}\right) = \mathfrak m \left({\tau}\right)$, where $\mathcal B$ denotes Borel $\sigma$-algebra, and $\mathfrak m$ denotes generated monotone class.