Tensorization of a Poincaré inequality
= Tensorization of a Poincaré inequality
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If each <probability measure> $\mu_i$ has <Poincaré inequality in probability theory>[Poincaré constant] $C_i$, then the <product measure> $\bigotimes_i\mu_i$ has <Poincaré inequality in probability theory>[Poincaré constant] at most $\max_iC_i$. This follows by iterating the <law of total variance> and applying <Jensen inequality> to derivatives of <conditional expectations>.