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 countably-valued functions, i.e., f ( t ) = lim n → ∞ f n ( t ) for almost every t , {\displaystyle f(t)=\lim _{n\rightarrow \infty }f_{n}(t){\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 ( { x } ) {\displaystyle f_{n}^{-1}(\{x\})} is measurable for each element x. The concept is named after Salomon Bochner.

Source: Wikipedia — Bochner measurable function (CC BY-SA 4.0)

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 countably-valued functions, i.e., f ( t ) = lim n → ∞ f n ( t ) for almost every t , {\displaystyle f(t)=\lim _{n\rightarrow \infty }f_{n}(t){\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 ( { x } ) {\displaystyle f_{n}^{-1}(\{x\})} is measurable for each element x. The concept is named after Salomon Bochner.

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Source: Wikipedia "Bochner measurable function" · CC BY-SA 4.0

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