2
$\begingroup$

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!

  • 0
    Be aware of notion of majorating: the function $f$ is a majorant for $g$ (both real-valued) if $f(x)\geq g(x)$ for all values $x$ of the argument. Example: optimal stopping and optimal control theory.2012-02-22
  • 0
    @Ilya: Thanks! Good to know.2012-02-22

1 Answers 1