The Entropy of the following distribution is $ - \infty $
$ p(x) = \frac{\delta(x=-1) + \delta(x=1)}{2} $
Mathematically the reason is because of having a $ - \infty \over 2 $ density probability for each of two spikes. What is the conceptual reason for having that Entropy value?
The Entropy measure: $ H(x) = - \int_{-\infty}^{+\infty} p(x).ln(p(x)).dx $
