ABSTRACT
This chapter focuses on the difference between the Riemann and Lebesgue iterated integrals. It discusses the convergence theorem of Lebesgue which plays a key role in integration theory. In various courses of mathematical analysis it is usually underlined that there is an essential advantage of the Lebesgue integral over the Riemann integral. In fact, one may observe a very good behavior of the Lebesgue integral with respect to standard operations of analysis and, first of all, with respect to the fundamental limit operation. The chapter also includes exercise problems related to Riemann and Lebesgue iterated integrals.
