Advantage of Lebesgue over Riemann integral

The authors made further research into Lebesgue integral,mainly dwelling on the advantages of Lebesgue integral over Riemann integral from three aspects.First,the scope of Lebesgue integral is wider than Riemann integral;Second,in a sense of Lebesgue integral,the condition of exchange order of integral limit is very weak;at last,the application scope of the basic differential integral theorem proves the result.