I have a problem with one question about Lebesgue-Stieljes measure. It is as follows:
$ρ(t) = (t − 1)^+$ for all $t ∈ \mathbb{R}$ is continuous and increasing, and the right derivative $ρ′_+(t) = ρ′(t+) = \textbf{1}_{[1,∞)}(t)$. Show that the Lebesgue-Stieltjes measure $m_p(dt) = \textbf{1}_{[1,∞)}(t)dt$ Note $(t-1)^+ = \max\{0, (t-1)\}$
What concerns me is the $dt$-bit in the statement as I'm not quite sure how to interpret it. From what I know, $m_p((s,t])=p(t)-p(s)$ but if as I said, do't really know what the $dt$ stands for.
Thanks!