Absolute Value of Simple Function is Simple Function/Proof 1

Proof
By Sum of Positive and Negative Parts, we have:


 * $\size f = f^+ + f^-$

We also have that Positive Part of Simple Function is Simple Function and Negative Part of Simple Function is Simple Function.

Hence $\size f$ is a pointwise sum of simple functions.

The result follows from Pointwise Sum of Simple Functions is Simple Function.