Tensorization (subadditivity) of entropy for product probability measures: $\mathrm{Ent}_{\otimes\mu_i}(h)\le\sum_i\int\mathrm{Ent}_{\mu_i}(h)\,d\mu$

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Tensorization (subadditivity) of entropy for product probability measures: $\mathrm{Ent}_{\otimes\mu_i}(h)\le\sum_i\int\mathrm{Ent}_{\mu_i}(h)\,d\mu$ · Prove2Me