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 countably-valued functions, i.e., f = lim n → ∞ f n for almost every t, {\displaystyle f=\lim _{n\rightarrow \infty }f_{n}{\text{ for almost every }}t,\,} where the functions f n {\displaystyle f_{n}} each have a countable range and for which the pre-image f n − 1 {\displaystyle f_{n}^{-1}} is measurable for each element x. Wikipedia