Definition 11.1.2 (Tagged Partition). Let $[a, b] \subset \real$, then a tagged partition of $[a, b]$ is a pair $(P = \seqfz{x_j}, c = \seqf{c_j})$ such that $c_{j} \in [x_{j - 1}, x_{j}]$ for each $1 \le j \le n$.

The collection $\scp_{t}([a, b])$ is the set of all tagged partitions of $[a, b]$.