Lebegue控制收敛定理的一种改进

An Improvement of Lebesgue’s Contral Covergence Theorem

对Lebegue控制收敛定理进行了改进,由此得到比Lebegue控制收敛定理更一般的结论,并对Fatou引理进行了推广,用推广的Fatou引理对改进后的Lebegue控制收敛定理给出了证明.

By improving the theory of Lebesgue＇s controlling covergence, we can draw a conclusion which is draw more intensive than the theory of Lebesgue＇s controlling covergence. We also generate Fatou＇s lemma. The improving theory of Lebesgue＇s controlling covergence can be proved by the generated Fatou＇s lemma.