ABSTRACT
This chapter discusses some natural extensions of results associated with the integral of a continuous function. It describes a sampling of what are generally referred to as Fubini theorems, theorems that involve the integration of functions of more than one variable. Enormous progress has been made in the field of analysis during the century, progress stemming in large part from the work of an outstanding French mathematician, Henri Lebesgue, at the beginning of the century. Lebesgue developed a new and more general approach to integration and his brilliant contributions brought about a substantial cohesiveness and simplicity to many areas of analysis. Leibniz considered integration and differentiation as inverse operations and presumed that integration determined the "net area" associated with the graph of the function being integrated. This attitude has prevailed almost intact to the present time and is seen as the major theme in most elementary treatments of the integral.
