I'm trying to prove that $(\mathbb{R},\mathcal{B}(\mathbb{R}),m_{\rho})$ is $\sigma$-finite.
Here, the $\sigma$-algebra is the Borel $\sigma$-algebra and $m_{\rho}$ is the Lebesgue-Stieltjes measure associated with an increasing right-continuous function $\rho$ on $\mathbb{R}$.
I'm getting really confused as to how to choose an appropriate cover for $\mathbb{R}$ since I barely know anything about $\rho$. Should I just take bounded sets?
I'd love any help, I really think I'm missing the point here!