Editing Measurable function (section)

== Term usage variations ==

The choice of <math>\sigma</math>-algebras in the definition above is sometimes implicit and left up to the context. For example, for <math>\R,</math> <math>\Complex,</math> or other topological spaces, the [[Borel algebra]] (generated by all the open sets) is a common choice. Some authors define '''measurable functions''' as exclusively real-valued ones with respect to the Borel algebra.<ref name="strichartz">{{cite book|last=Strichartz|first=Robert|title=The Way of Analysis|url=https://archive.org/details/wayofanalysis0000stri|url-access=registration|publisher=Jones and Bartlett|year=2000|isbn=0-7637-1497-6}}</ref>

If the values of the function lie in an [[infinite-dimensional vector space]], other non-equivalent definitions of measurability, such as [[weak measurability]] and [[Bochner measurability]], exist.