Bochner measurable

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 ${\displaystyle f_{n}}$ each have a countable range and for which the pre-image ${\displaystyle f^{-1}\{x\}}$ is measurable for each x. The concept is named after Salomon Bochner.

Bochner-measurable functions are sometimes called strongly measurable, ${\displaystyle \mu }$-measurable or just measurable (or uniformly measurable in case that the Banach space is the space of continuous linear operators between Banach spaces).

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