H ( X ) + H ( f ( X ) | X ) = H ( f ( X ) ) + H ( X | f ( X ) ) , {\displaystyle \mathrm {H} (X)+\mathrm {H} (f(X)|X)=\mathrm {H} (f(X))+\mathrm {H} (X|f(X)),} so H ( f ( X ) ) ≤ H ( X ) {\displaystyle H(f(X))\leq H(X)} , the entropy of a variable can only decrease when the latter is passed through a function.