Take some real valued continuous random variable $X$ with CDF $F$. Take a function $G:\mathbb{R}\to \mathbb{R}$ defined as
$$G(z)=\int^\infty_z xdF(x)=\mathbb{E}[X|X\geq z] \mathbb{P}(X\geq z).$$
Does $G$ have a name? Apologies if this is not an appropriate question for this site but I don't want to make up a name for it if there is a known nomenclature for it.