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Suppose we have two random variables: $X \sim f(x)$ and $X' \sim f'(x)$ and we know how to compute $KL(f||f')$. We apply a one to one function $g$ on both random variables which gives us two new variables: $Y \sim h(y)$ and $Y'\sim h'(y)$. Is there any closed from relation for $KL(h||h')$ based on $KL(f||f')$?

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