In machine learning the following function is used pretty often: $$ f(x) = \left\{\begin{matrix} g(x) & x > 0\\ h(x) & x \leqslant 0 \end{matrix}\right.$$
Is there a standard more compact notation? Something like $\varsigma \left ( g(x), h(x) \right )$.
As far as I can tell, no. The closest you can get is writing $$ f(x) = \mathbb{1}_{x\leq 0}(x) \cdot h(x) + \mathbb{1}_{x>0}(x)\cdot g(x) $$ where $1_A: A \to \{0, 1\}$ is the Indicator function.