Before asking i would like to present the following:
We now that the average power for an ergodic stochastic process $X=\{X_t(\omega)\}_{t\in T}$ is $$P= \lim_{\tau\to\infty}\int_{-\infty}^\infty\frac{1}{2\tau} \mathbb{E}\{|\hat{X}^\tau(f)|^2\}df$$ where $$\hat{X}^\tau(f)=\int_{-\infty}^{\infty}X^\tau e^{-i2\pi ft}dt$$ and, $$ X^\tau= X\chi_{(-\tau,\tau)}=\begin{cases} X_t & |t|<\tau \\ 0 & |t|>{\tau} \end{cases}.$$
What I want to ask is: As the process is assumed to be ergodic, can we interchange the order of $\lim_{\tau\to\infty}$ and $\int_{-\infty}^\infty$? If yes, why?
I'm really new to stochastic processes and I'm studying on my own. Any help would be appreciated!