Comparison Between Riemann Integral and Lebesgue Integral

This article researches the relations between Riemann integral and lebesgue integral.While giving out the relations between Riemann integral and Lebesgue integral,the paper puts the relations between improper Riemann integral and Lebesgue integral.That in when function )(xf is Riemann integrabel in closed interval ],[ba,it also Lebesgue integrabel in closed interval ],[ba, and the value of the two integral is infinite integral or improper integral of limitless function is absolutely convergent in the interval.function )(xf is Lebesgue integrabel in the interval,and the value of the two integral is equivalent;While infinite integral or improper integral of limitless function is conditionally convergent in the interval.function )(xfis not Lebesgue integrabel in the interval.