Difference between revisions of "Positive and negative parts of a function"
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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]:
- [ilmath]f^+:=\max(f,0)[/ilmath] defined pointwise, so [ilmath]f^+(x)=\max(f(x),0)[/ilmath]
- [ilmath]f^-:=-\min(f,0)[/ilmath] defined pointwise, so [ilmath]f^-(x)=-\min(f(x),0)[/ilmath]
Then:
- [ilmath]f=f^+-f^-[/ilmath]
References
- ↑ Probability and Stochastics - Erhan Cinlar
