## Definition 7.4.12: Measurable Function

Let

*f*be a function from*into***E****R***. The function**{ -, }***R***f*is called (Lebesgue) measurable if- the domain
of the function is a measurable set**E** - for every real number
*a*the set*f*is a measurable set^{ -1 }(-, a)