Generalised N-dimensional Riemann Sum

Let I=[a1,b1]××[aN,bN] be an N-cell in N. For each j=1,,N, let aj=tj,0<<tj,N=bj be a partitionMathworldPlanetmathPlanetmath Pj of [aj,bj]. We define a partition P of I as


Each partition P of I generates a subdivision of I (denoted by (Iν)ν) of the form


Let f:UM be such that IU, and let (Iν)ν be the corresponding subdivision of a partition P of I. For each ν, choose xνIν. Define


As the Riemann sum of f corresponding to the partition P.

A partition Q of I is called a refinement of P if PQ.

Title Generalised N-dimensional Riemann Sum
Canonical name GeneralisedNdimensionalRiemannSum
Date of creation 2013-03-22 13:37:40
Last modified on 2013-03-22 13:37:40
Owner vernondalhart (2191)
Last modified by vernondalhart (2191)
Numerical id 4
Author vernondalhart (2191)
Entry type Definition
Classification msc 26B12