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Pettis theorem : ウィキペディア英語版
Weakly measurable function
In mathematics — specifically, in functional analysis — a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree.
==Definition==

If (''X'', Σ) is a measurable space and ''B'' is a Banach space over a field K (usually the real numbers R or complex numbers C), then ''f'' : ''X'' → ''B'' is said to be weakly measurable if, for every continuous linear functional ''g'' : ''B'' → K, the function
:g \circ f \colon X \to \mathbf \colon x \mapsto g(f(x))
is a measurable function with respect to Σ and the usual Borel ''σ''-algebra on K.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Weakly measurable function」の詳細全文を読む



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