Let $X$ be a random variable with some distribution $f\_X(x)$, and assume that we generate $X\_1, \ldots, X\_N$ i.i.d. samples from this distribution. For simplicity, assume $X\_n \in \mathbb{R}$.

Then it is clear from elementary probability theory:

$$\mathbb{E}(X) = \int\limits\_{-\infty}^\infty x f\_X(x) dx$$

If we have a function $g$, then

$$\mathbb{E}(g(X)) = \int\limits\_{-\infty}^\infty g(x) f\_X(x) dx$$

Suppose now we associate each sample $X\_i$ with a label $y\_i \in \{-1,+1\}$ and form the set: 

$$\mathcal{D} = \{(X\_1, y\_1), \ldots, (X\_N, y\_N)\}$$

which we can refer to as a "data set".

My question is, what is 

$$\mathbb{E}(\mathcal{D})?$$

[I have seen multiple references that takes expectation with respect to the data set](https://homes.cs.washington.edu/~pedrod/papers/mlc00a.pdf), however, I have never seen a closed form expression of $\mathbb{E}(\mathcal{D})$

Is $\mathcal{D}$ a random variable? A set of scalars? How do we make sense of $\mathbb{E}(\mathcal{D})$?