Recently, the locally convex space theory has obtained a series of proper developments and improvements by the agency of the Basic Matrix Theorem (BMT) duc to J. Mikusinski and P. Antosik. In this note, we would like ...Recently, the locally convex space theory has obtained a series of proper developments and improvements by the agency of the Basic Matrix Theorem (BMT) duc to J. Mikusinski and P. Antosik. In this note, we would like to present another basic theorem named Uniform Convergence Principle (UCP). We shall show that UCP has the same effects as BMT, though UCP is easier than BMT in their proofs. UCP. Let G be an abelian topological group and Ωa sequentially compact space.展开更多
设{ξ1,ξ2,…,ξn}为来自[0,1]上服从均匀分布的独立同分布样本,产生的经验过程为Fn(t)=n^(-1/2)sum from i=1 to n( (I{ξi≤t}-t)),0≤t≤1,‖Fn‖=sup 0≤t≤1 Fn(t).利用经验过程的弱收敛定理和尾概率不等式,对一般的边界函数和拟...设{ξ1,ξ2,…,ξn}为来自[0,1]上服从均匀分布的独立同分布样本,产生的经验过程为Fn(t)=n^(-1/2)sum from i=1 to n( (I{ξi≤t}-t)),0≤t≤1,‖Fn‖=sup 0≤t≤1 Fn(t).利用经验过程的弱收敛定理和尾概率不等式,对一般的边界函数和拟权函数得到了矩完全收敛性精确渐近性的一般形式.展开更多
基金Supported by the National Natural Science Foundation of China(10661001)partially by the Guangxi Natural Science Foundation(0832275)the Natural Science Foundation of Liuzhou Teacher's College(LSZ2007A003)
文摘Recently, the locally convex space theory has obtained a series of proper developments and improvements by the agency of the Basic Matrix Theorem (BMT) duc to J. Mikusinski and P. Antosik. In this note, we would like to present another basic theorem named Uniform Convergence Principle (UCP). We shall show that UCP has the same effects as BMT, though UCP is easier than BMT in their proofs. UCP. Let G be an abelian topological group and Ωa sequentially compact space.
文摘设{ξ1,ξ2,…,ξn}为来自[0,1]上服从均匀分布的独立同分布样本,产生的经验过程为Fn(t)=n^(-1/2)sum from i=1 to n( (I{ξi≤t}-t)),0≤t≤1,‖Fn‖=sup 0≤t≤1 Fn(t).利用经验过程的弱收敛定理和尾概率不等式,对一般的边界函数和拟权函数得到了矩完全收敛性精确渐近性的一般形式.
