I was wondering what the definitions of one mapping dominating another in some general settings are?
A special case I inferred from Dominated Convergence Theorem is that: for mappings $f$ and $g$ from a set $X$ to $\mathbb{R}$, $f$ is called to dominate $g$, if for every $x \in X$, $f(x) \geq |g(x)|$.
Can we generalize their codomain from $\mathbb{R}$?
Generally, does it require the dominating function $f$ to be a nonnegative function?
Thanks and regards!