ThmDex – An index of mathematical definitions, results, and conjectures.
Partition of basic function into positive and negative parts
Formulation 0
Let $f : X \to [- \infty, \infty]$ be a D3180: Basic function such that
(i) $f^+$ is the D1289: Basic function positive part of $f$
(ii) $f^-$ is the D1290: Basic function negative part of $f$
Then \begin{equation} f = f^+ - f^- \end{equation}