Measurability of an integral operator?!

Question

Is it possible to prove the measurability of the following map $\Phi_n \colon (C(\mathbb{R}^d), \sigma(\mathcal{C})) \to (\mathbb{R}, \mathcal{B}(\mathbb{R}))$, $n \in \mathbb{N}$, defined by $$ \Phi_n(f) := \int_{[-n,n]^d} |f(x)|^2 \, dx, \quad f \in C(\mathbb{R}^d), $$ where $\mathcal{C}$ is the collection of finite-dimensional cylinder sets. Note that $C(\mathbb{R}^d)$ is endowed with the metric $$ \rho(f,g) = \sum_{n=1}^\infty \frac{1}{2^n} \frac{\rho_n(f,g)}{1+\rho_n(f,g)} , \quad \rho_n(f,g) := \sup_{x \in [-n,n]^d} |f(x) - g(x)|, $$ making $C(\mathbb{R}^d)$ a complete, separable metric space. I thought about proving pointwise continuity of $\Phi_n$, but that didn't go anywhere so far. Maybe someone has an idea? I only need measurability after all. Or perhaps it's not even correct...