stylistic:tone, information:extraction, information:classification
Generalization

In high generality, Riemann sums can be written S = ∑ i f (P i ∗) μ (V i), {\displaystyle S=\sum _{i}f(P_{i}^{*})\mu (V_{i}),} where P i ∗ {\displaystyle P_{i}^{*}} stands for any arbitrary point contained in the set V i {\displaystyle V_{i}} and μ {\displaystyle \mu } is a measure on the underlying set. Roughly speaking, a measure is a function that gives a "size" of a set, in this case the size of the set V i {\displaystyle V_{i}}; in one dimension this can often be interpreted as a length, in two dimensions as an area, in three dimensions as a volume, and so on.