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Can somebody please explain the math behind this statement to me? I am not sure how they represent the left hand side by that integral and finally how it is proportional to that.
\begin{align}
p(S_{t+1}|z_{t+1}) &=\int p(S_{t+1}|S_t,z_{t+1})d\mathbb{P}(S_t|z^{t+1}) \\
&\propto...