Show that if $\sum_{y \in S^c} \pi(y) = \sum_{y \in S^c} \sum_{x \in \Omega} \pi(x)P(x, y)$ for any $S \subset \Omega$.
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We are given that $\sum_{y \in S^c} \pi(y) = \sum_{y \in S^c} \sum_{x \in \Omega} \pi(x)P(x, y)$. We want to show that this equation holds for any $S \subset \Omega$. Show more…
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