Abstract
It is shown that if X 1 , X 2 , … X_1,X_2,\ldots are independent and identically distributed square-integrable random variables, then the entropy of the normalized sum \[ Ent ( X 1 + ⋯ + X n n ) \operatorname {Ent} \left (\frac {X_{1}+\cdots + X_{n}}{\sqrt {n}} \right ) \] is an increasing function of n n . The result also has a version for non-identically distributed random variables or random vectors.
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