Let $G$ be a discrete group. A $G$-space $X$ is called a $G$-boundary if the action $G \curvearrowright X$ is minimal and strongly proximal. In this talk, we shall prove a continuous version of the well-studied Intermediate Factor Theorem in the context of measurable dynamics. When a product group $G = \Gamma_1 \times \Gamma_2$ acts (by a product action) on the product of corresponding $\Gamma_i$-boundaries $\partial \Gamma_i$, we show that every intermediate factor $$X \times (\partial \Gamma_1 \times \partial \Gamma_2) \rightarrow Y \rightarrow X$$ is a product (under some additional assumptions on $X$). We shall also compare it to its measurable analog proved by Bader-Shalom. This is a recent joint work with Yongle Jiang.