\begin{definition}[Definition:Differential Entropy]
'''Differential entropy''' extends the concept of entropy to continuous random variables.
Let $X$ be a continuous random variable.
Let $X$ have probability density function $f_X$. 
Then the '''differential entropy''' of $X$, $\map h X$ measured in nats, is given by: 
:$\ds \map h X = -\int_{-\infty}^\infty \map {f_X} x \ln \map {f_X} x \rd x$
Where $\map {f_X} x = 0$, we take $\map {f_X} x \ln \map {f_X} x = 0$ by convention.
\end{definition}