[分析] characterization of weakly measurable functions
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.
類比於 storngly measurable 的定義, 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'.
不知道這個猜測是否正確?
<= 方向的證明很簡單, 但是 => 卻沒有頭緒...
懇請板上神人指點迷津!
感謝!!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.133.4.190