The Shannon entropy $I(P)$ of a probability vector $P \in [0,1]^{n}$ is given by
$I(P) = - \sum_{\gamma = 1}^{n} P_{\gamma} ln(P_{\gamma})$
I want to show that $I(P)$ is well defined i.e., $lim_{x \rightarrow 0} xln(x) = 0$
Does someone have any idea how can I do that? Thanks!
