Tagged partition

A tagged partition of $[a,b]$ is a partition $P=\{x_0,\dots,x_n\}$ together with a choice of points (tags) $t_i\in[x_{i-1},x_i]$ for each $i=1,\dots,n$. It is often denoted $(P,\{t_i\}_{i=1}^n)$.

Tagged partitions are the input data for a Riemann sum and, more generally, for a Riemann–Stieltjes sum .

Examples:

• (Midpoint tags) For each $i$, take $t_i=\tfrac12(x_{i-1}+x_i)$.
• (Right-endpoint tags) For each $i$, take $t_i=x_i$.