摘要
设(E,S,Ω,f)是随机结构空间,当(E,S,Ω,f)是随机度量空间,随机赋范空间,随机内积空间时,其向量的随机度量,随机范数,随机内积是随机变量.证明了它们的数学期望分别是拟度量,拟范数,内积.应用关于数学期望的结果,进而得到了随机Hilbert空间中线性连续泛函的Riesz表示定理.
Let (E, S, Ω, f) be an random structure space, when (E,S,Ω,f) is random metric space, then random metric is random variable. The mathematical expectation of random metric is quasi-metric. When (E,S,Ω,f) is random normed space, then random norm is random variable. The mathematical expectation of random norm is quasi-norm. When (E,S,Ω,f) is random inner product space, then random inner product is random variable. The mathematical expectation of random inner product is inner product. Further, the Riesz theorem of contiuous linear functional is proved by using mathematical expectation of random inner product.
出处
《应用泛函分析学报》
CSCD
2005年第1期76-82,共7页
Acta Analysis Functionalis Applicata
基金
天津市学科建设基金(100580204)
关键词
随机度量
随机内积
随机变量
数学期望
表示定理
随机拓扑空间
random metric
random norm
random inner product
random variable
mathematical expectation
riesz theorem
