作者Rhymer (Design)
看板Math
标题[分析] characterization of weakly measurable functions
时间Sat Jun 11 18:19:03 2011
Let (Ω,Σ) be a measurable space and X a Banach space.
f:Ω->X is called weakly measurable if for each linear functional
x' in X'(the norm dual of X),
the scalar function < f, x' > is measurable.
类比於 storngly measurable 的定义, 我猜想
f is weakly measurable iff there exists a sequence of step functions
φ_n:Ω->X such that < φ_n, x' > converges to < f, x' > for each x' in X'.
不知道这个猜测是否正确?
<= 方向的证明很简单, 但是 => 却没有头绪...
恳请板上神人指点迷津!
感谢!!
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 220.133.4.190