Mesh of a partition

Definition

Let $P = (x_0, \dots, x_n)$ be a partition of $[a, b]$ . The mesh of $P$ is $\| P \| = \max_{1 \le i \le n} (x_i - x_{i-1}),$ the length of the longest subinterval of $P$ .

Remarks

Refining a partition does not increase its mesh. The Riemann integral is a limit of Riemann sums as the mesh tends to $0$ . For the partition of $[0, 1]$ into $n$ equal pieces, the mesh is $1/n$ .

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Partition of an interval definition
Mesh of a partition definition

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Tag	`04GM4NYXJB`
URI	`m2://04GM4NYXJB`
Aliases	`norm-of-a-partition`
Kind	definition
Writing	W0 stub
MSC	26A42
Defines	Mesh of a partition
Uses	Partition of an interval

Mesh of a partition

Definition

Remarks

Reading path

Where this leads

Further reading

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