Measure theory MOC

Measurable function

A measurable functions is a structure-preserving map of measurable spaces. Let and be measurable spaces. A function is called measurable iff the preïmage of every measurable set is measurable¹ , measure i.e. for any .

Properties

1. A measurable function from a measure space induces a Pushforward measure on its codomain.

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Footnotes

1. Note this is analogous to the topological definition of Continuity. ↩