What kind of entity is the expectation of a random variable?

Question

Given a probability space $(Ω, \mathcal F, P)$ and an integrable random variable $ξ: Ω \to \Bbb R$, what kind of entity is the expectation of $ξ$ i.e. $E(ξ)=\int_Ω ξdP$? My sense is that we have a functional (or an operator) $RV\mapsto\Bbb R$, where $RV\subseteq F:=\{f|f \space \mathrm {function}\}$ is the set of random variables. I found nowhere in bibliography a characterization of expectation 's nature.