About: Bochner measurable function

In mathematics – specifically, in functional analysis – a Bochner-measurable function taking values in a Banach space is a function that equals almost everywhere the limit of a sequence of measurable , 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 in case that the Banach space is the space of continuous linear operators between Banach spaces).