## 7.4. Lebesgue Integral

### Example 7.4.14(d): Measurable Functions

Show that a function

*f*is measurable if and only if- the set
*{ x: f(x) < a }*is measurable for all*a* - the set
*{ x: f(x) a }*is measurable for all*a* - the set
*{ x: f(x) > a }*is measurable for all*a* - the set
*{ x: f(x) a }*is measurable for all*a*