# Multiple Integrals

• Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Let [a, b] be a closed interval. We recall that a partition P on [a, b] is a finite sequence of numbers
$$a = {c_0}\underline{\underline < } {c_1}\underline{\underline < } ...\underline{\underline < } {c_r} = b$$
between 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
$${J_1} \times ... \times {J_n}$$
of closed intervals 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.