Is a discrete random process issued from a sampled continuous ergodic WSS process also ergodic?

Question

I have a continuous time process $\{X_t,t\in\mathbb{R}\}$ that is WSS and ergodic for the 1st and 2nd moments.

I create a random discrete process $\{Y_n,n\in\mathbb{N}\}=\{X_t,t=nT\}$ by discretizing $\{X_t\}$. It follows that the discrete process $\{Y_n\}$ is also WSS.

But, is $\{Y_n\}$ also ergodic?

Thanks for your contributions,

Nicolas