Positive and negative parts of a function

---

TODO: Flesh out this page, it's currently only to document something found in Probability and Stochastics

---

Definition

We define the positive and negative parts of a function as follows:

• $f^+:=\max(f,0)$ defined pointwise, so $f^+(x)=\max(f(x),0)$
• $f^-:=-\min(f,0)$ defined pointwise, so $f^-(x)=-\min(f(x),0)$

Then:

• $f=f^+-f^-$