可积函数空间L^P中的几种收敛性关系

Relationship Between Several Convergences in Integrable Function Space L^p

文章对可积函数空间L^P中强收敛、弱收敛和依测度收敛几种收敛的定义和性质进行归纳和总结,讨论他们之间的关系,并给出了相应结果的证明,从而使各种收敛关系更加明晰和透彻。

The definitions and properties of strong convergence, weak convergence and convergence in measure of integrable function space L^p are generalized in the paper. We discussed their interrelationship and gave some proofs about the corresponding results, which made the connections between them more clear and thorough.