Banach空间中强可测函数的选择定理  

Selection Theorm of Strongly Measurable Functions in Banach Space

作　　者：张筱玮[1] 

机构地区：[1]天津教育学院,天津300020

出　　处：《河北大学学报（自然科学版）》1998年第S1期24-26,共3页Journal of Hebei University(Natural Science Edition)

摘　　要：对Banach空间中强可测函数的选择性进行了研究,得到如下结果:设f(t)为[0,1]到X(Banach空间X的对偶空间)的强可测函数,则对任意0<ε<1,存在由[0,1]到X的强可测函数g_g(t),使|g_g(t)|≤1,且(f(t),g_g(t))≥(1-ε)‖f(t)‖在[0,1]上几乎处处成立。并进而证明:若X为自反的Banach空间,则存在强可测函数g(t),使(f(t),g(t))=‖f(t)‖且‖g(t)‖=1在[0,1]上几乎处处成立。Discussed selection theorems for strongly measurable functions in Banach space and showedfollowing statement: if f(t) is a strongly measurable function from [0, 1] to X*, than for any 0<ε<1,there is a strongly measurable functiong,(t) from [0,1] to X,such that||g(?)(t)≤1|| and (f(t), g(?)(t))≥(1-ε) ||f(t) ||, a. e on [0, 1] .The point is also pointed out in the paper: when X is a reflexive Banach space,there exists a strongly measurable functiong(t) satisfying (f(t), g(t)) = || f(t) || and ||g(t) ||= 1.a.eon [0,1].

关 键 词：BANACH空间 强可测的 

分 类 号：O177.2[理学—数学]