Definition 5.1.2 (Tagged Partition).label Let $[a,b]\suf\R$ then a tagged partition of $[a,b]$ is a pair $(P=\curl{x_j}^{n}_{j=0}, c=\curl{c_j}^{n}_{j=0})$ such that $c_{j}\in [x_{j-1},x_{j}]$ for each $1\leq j\leq n$. The collection $\scr{P}_{t}([a,b])$ is the set of all tagged parititions of $[a,b]$.