积分中值定理在广义Riemann积分中的推广

An Extension of the First Mean Value Theorems for Generalized Riemann Integration

文章按着如下方式将积分第一中值定理在广义Riemann积分中做了推广.如果在开区间I(?)R上f(x)有界连续,g(x)非负可积(广义),则对(?)ε>0,(?)ξ∈I使得|∫_If(x)g(x)dx-f(ξ)∫_Ig(x)dx|<ε.

This article discusses two theorems in the following way. If f(x) is a bound continuity, and g (x) is not a negative generalized Riemann integrable on the open interval I(?)R , then I ful-fills .