Theorem 1: let $(X_n, n \in \mathbb{Z})$ - centered, weakly(or "wide-sense") stationary stochastic process. Then there is centered orthogonal random measure $Z$ on $\mathcal{B}([-\pi, \pi])$ such that $\forall n \in \mathbb{Z}$ we have equality:
$\begin{align} X_n = \int_{-\infty}^{\infty}e^{in\lambda}Z(d\lambda) \end{align}$
The second one is similar, but for processes parametrized by $t \in \mathbb{R}$:
Theorem 2: let $(X_t, t \in \mathbb{R})$ - centered, weakly(or "wide-sense") stationary, $L^2$-continuous stochastic process. Then there is centered orthogonal random measure $Z$ on $\mathcal{B}(\mathbb{R})$ such that $\forall t \in \mathbb{R}$ we have equality:
$\begin{align} X_t = \int_{\mathbb{R}}e^{in\lambda}Z(d\lambda) \end{align}$
These are called "spectral representations" as I would translate them.
The problem is that it seems like mathematicians in my area especially love this branch of st.processes, so they put it in almost every textbook about it, and as one then would guess, I'm likely to have a problem on this topic on the test. I'm used to rely much on english sources, but when I search for this theorem, or even related questions - it's very hard to find something.
I'm not even sure if one can easily find notion of "orthogonal random measure". If you wanted to know what it means in local books, I will try to give a translation. It seems to be intuitively clear what $L^2$-continuity is. Thank you.