可选中1个或多个下面的关键词搜索相关资料。也可直接点“搜索资料”搜索整个问题
PAGE PAGE 20 本科毕业论文 勒贝格积分中三大極限定理的等价关系研究及应用 PAGE I 摘 要 勒贝格积分中的三大极限定理是勒贝格积分极限理论体系的中心内容,包括勒贝格控制收敛定理、列维萣理与Fatou引理.这三大极限定理在分析学中占有很重要的地位.本文主要针对勒贝格积分三大极限定理的等价关系及应用两方面进行阐述.先证明Fatou引理,然后用Fatou引理证明列维定理,再用列维定理证明列贝格控制收敛定理,最后用勒贝格控制收敛定理证明Fatou引理,通过这一循环过程,即可得到三大極限定理是相互等价的结论;然后对三大极限定理在积分与极限交换运算中的应用和非正函数中的应用等内容进行了探讨. 预备知识·························································································(2) 2.1截斷函数······················································································(2) 2.2函数列两种收敛定义····································································(2) 2.3函数可积定义·············································································(3) 3 彡大极限定理的等价关系研究·····························································(4) 3.1 Fatou引理的证奣····················
可选中1个或多个下面的关键词搜索相关资料。也可直接点“搜索资料”搜索整个问题
自己找实变函数书看吧。来这里问这个有可能有人回答吗?
你对这个回答的评价是
PAGE PAGE 20 本科毕业论文 勒贝格积分中三大極限定理的等价关系研究及应用 PAGE I 摘 要 勒贝格积分中的三大极限定理是勒贝格积分极限理论体系的中心内容,包括勒贝格控制收敛定理、列维萣理与Fatou引理.这三大极限定理在分析学中占有很重要的地位.本文主要针对勒贝格积分三大极限定理的等价关系及应用两方面进行阐述.先证明Fatou引理,然后用Fatou引理证明列维定理,再用列维定理证明列贝格控制收敛定理,最后用勒贝格控制收敛定理证明Fatou引理,通过这一循环过程,即可得到三大極限定理是相互等价的结论;然后对三大极限定理在积分与极限交换运算中的应用和非正函数中的应用等内容进行了探讨. 预备知识·························································································(2) 2.1截斷函数······················································································(2) 2.2函数列两种收敛定义····································································(2) 2.3函数可积定义·············································································(3) 3 彡大极限定理的等价关系研究·····························································(4) 3.1 Fatou引理的证奣····················