Riemann积分与Lebesgue积分的本质区别

The essential difference of Riemann calculus and Lebesgue calculus

指出Riemann积分与Lebesgue积分的本质区别在于:区间[a,b]上所有Riemann可积函数所生成的空间是不完备的,而所有Lebesgue可积函数所生成的空间是完备的．

The article points out the essential difference of Riemann calculus and Lebesgue calculus is that the space in which all Riemann integral functions formed is incomplete, but the space in which all Lebesgue integral functions formed is complete.