关于Lebesgue积分极限理论体系的教学方法探讨

本文对Lebesgue积分极限理论体系的教学方法作了探讨．指出该理论体系的核心定理是Levi单调收敛定理，再由核心定理推导其它定理将使该理论体系简洁明了，找到本质所在可起到事半功倍的作用．同时指出目前国内普遍采用的《实变函数论》教程中关于三大Lebesgue积分极限定理相互等价的说法具有不妥之地

The Pedagogy Discussion on Lebesgue Intergration Limit Theory

In this paper, we discussed the pedagogy on Lebegue intergration limit theory. We pointed out that the monotone covergence theorem is kernel theorem for series of intetgration limit theorem. We also showed that monotone convergence theorem and Lebesgue dominated convergence theorem are not equivalent.