## 7.1. Riemann Integral

### Definition 7.1.1: Partition of an Interval

A

**partition***P*of the closed interval*[a, b]*is a finite set of points*P = { x*such that_{0}, x_{1}, x_{2}, ..., x_{n}}The maximum difference between any two consecutive points of the partition is called thea = x_{0}< x_{1}< x_{2}< ... < x_{n-1}< x_{n}= b

**norm**or**mesh of the partition**and denoted as*| P |*, i.e.A| P | = max { x_{j}- x_{j-1}, j = 1 ... n }

**refinement of the partition**is another partition*P**P'*that contains all the points from*P*and some additional points, again sorted by order of magnitude.