摘要
作为综合运用测度的积分控制收敛定理和线性连续泛函的延拓定理（简称控制收敛定理和延拓定理）的范例，本文首先给出广义Ｆ．Ｒｉｅｓｚ定理，再从构造变差函数着手，用分析的方法证明广义Ｆ．Ｒｉｅｓｚ定理。
Summary:Being an example in applying comprehensirely bominated convergence theorem of integral measure and extension theorem of linear otnicnuity function,this paper first generalizes F.Riesz Theorem and thenproves it by way of construct ion functional analysis.
