ABSTRACT
A substantial amount of Integration theory of functions of one variable carries over to the case of functions defined on a subset of ℝn. Nevertheless, there are some important differences, and the proper theory of the multiple integrals was fully developed only at the end of the nineteenth century, in the work of Thomae, Peano, and Jordan. When defining the double integral, in this chapter, the author follows the pattern used for the definite integral of a single variable function. The author focuses on the situation when the integrand is a non-negative function. In other words, the author studies the absolute convergence of the integrals. Towards the author explains the reason for this attitude.
