I'm having bit trouble in understanding weak convergences in Bochner space. I have following question for some general measurable space $\Omega$:

Let $\{x_n\}$ be a bounded sequence in $L^2((0,T)\times \Omega ; H^1(\mathbb{R}^d))$, then we can extract a weakly convergent sub sequence $\{x_{n_k}\}$ st $x_{n_k} \rightharpoonup x $ in $L^2((0,T)\times \Omega ; H^1(\mathbb{R}^d))$. Can we conclude for a.e. $t$, $x_{n_k}(t) \rightharpoonup x(t) $ in $L^2(\Omega ; H^1(\mathbb{R}^d))$?