What is an example of a simple borel measurable function?

Answer 1

Characteristic function of any borel set is an example of simple Borel function

Answer 2

One example of a simple Borel measurable function is the indicator function of a Borel set. This function takes the value 1 on the set and 0 outside the set, making it easy to determine its measurability with respect to the Borel sigma algebra.