Tagged Partition of a Closed Interval

Let $a,b\in\mathbb{R}$ with $a<b$, and let $P=(x_0,x_1,\dots,x_n)$ be a partition of $[a,b]$. A tagged partition of $[a,b]$ relative to $P$ is a choice of points $t_i\in[x_{i-1},x_i]$ for each $i=1,\dots,n$.