Difference between revisions of "Positive and negative parts of a function"

Latest revision as of 01:21, 5 August 2015

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^[1]:

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

Then:

• $f=f^+-f^-$

References

1. Jump up ↑ Probability and Stochastics - Erhan Cinlar