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In mathematics – specifically, in functional analysis – a Bochner-measurable function taking values in a Banach space is a function that equals a.e. the limit of a sequence of measurable countably-valued functions, i.e., : where the functions each have a countable range and for which the pre-image is measurable for each ''x''. The concept is named after Salomon Bochner. Bochner-measurable functions are sometimes called strongly measurable, -measurable or just measurable (or uniformly measurable in case that the Banach space is the space of continuous linear operators between Banach spaces). ==Properties== The relationship between measurability and weak measurability is given by the following result, known as Pettis' theorem or Pettis measurability theorem.
In the case that ''B'' is separable, since any subset of a separable Banach space is itself separable, one can take ''N'' above to be empty, and it follows that the notions of weak and strong measurability agree when ''B'' is separable. 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「Bochner measurable function」の詳細全文を読む スポンサード リンク
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