Let $D$ be a compact topological space with Borel $\sigma$-algebra $\mathcal{B}(D)$.
Let the space of bounded measurable functions from $D$ to $\mathbb{R}$ $$ \mathbb{R}^{D}_b: = \{f : D \to \mathbb{R} \mid f \text{ is bounded and $\mathcal{B}(D)/\mathcal{B}(\mathbb{R})$-measurable} \} $$ be equipped with the topology induced by the sup-norm $\lVert \cdot \rVert_{\infty}$ as well as the resulting canonical Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R}^{D}_b)$.
Now let us define a map $$ \Phi : \mathbb{R}^{D}_b \times D \to \mathbb{R}, \quad \Phi(f,\pi) = f(\pi) .$$
Is it true, that $\Phi$ is $(\mathcal{B}(\mathbb{R}^{D}_b) \otimes \mathcal{B}(D))/\mathcal{B}(\mathbb{R})$-measurable? How could I show this?