Riemann积分与Lebesgue积分的本质区别

Riemann′s Integration is Differentiateed Against Lebesgue′s Integration Nature

对Riemann积分与Lebesgue积分的本质区别进行了研究。得出二者的本质区别为:区间上所有Rie-mann可积函数所生成的空间不是完备的,而所有Lebesgue可积函数所生成的空间是完备的,并对此结论进行了证明。

Text is aimed at the Lebesgue＇s integration and Riemann＇s integration＇s nature difference has been underway research, proposeing the nature of differentiated of tow knowledge：Area [ a, b ] all the Riemann＇s summable function formations spaces are not complete, But all the Lebesgue＇s summable function formations spaces are complete, and proving this conclusion.