The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In...The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.展开更多
We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent t...We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems.展开更多
基金Supported by Research Fund of Kumoh National Institute of Technology(M1100)
文摘The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.
基金This project is supported by NSFC(10471124)is supported by Zhejiang Provineial Natural Science Foundation of China(M103057)sponsored by SRF for ROCS,SEM
文摘We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems.
