Undergraduate Analysis pp 469-509 | Cite as

# Multiple Integrals

Chapter

## Abstract

Let [ between of closed intervals

*a*,*b*] be a closed interval. We recall that a partition*P*on [*a*,*b*] is a finite sequence of numbers$$
a = {c_0}\underline{\underline < } {c_1}\underline{\underline < } ...\underline{\underline < } {c_r} = b
$$

*a*and*b*, giving rise to closed subintervals [*c*_{ i },*c*_{ i }_{+1}]. This notion generalizes immediately to higher dimensional space. By a**closed***n*-**rectangle**(or simply a rectangle) in**R**^{ n }we shall mean a product$$
{J_1} \times ... \times {J_n}
$$

*J*_{1}, ... ,*J*_{ n }. An open rectangle is a product as above, where the intervals*J*_{ i }are open. We shall usually deal with closed rectangles in what follows, and so do not use the adjective “closed” unless we start dealing explicitly with other types of rectangles.## Keywords

Vector Field Variable Formula Multiple Integral Admissible Function Inverse Mapping Theorem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1983