Definition:Uncertainty/Also defined as

Uncertainty: Also defined as

In their definition of uncertainty, some sources do not specify the condition that the summation is over those $k$ where $p_k > 0$, but instead define $0 \lg 0 = 0$.

This is justified as:

$\ds \lim_{x \mathop \to 0^+} x \lg x = 0$

from Limit of Power of $x$ by Absolute Value of Power of Logarithm of $x$: Corollary.