Prove the information inequality (Lemma 9.1) by applying Jensen’s inequality (−log x is convex) to the function log[f (y)/g(y)]. Recall that equality is reached with Jensen if the function is linear;...

Prove the information inequality (Lemma 9.1) by applying Jensen’s inequality (−log x is convex) to the function log[f (y)/g(y)]. Recall that equality is reached with Jensen if the function is linear; and these must be densities. Also consider the case when the supports are different.