-3
votes
1answer
60 views

What's the Shannon entropy of the prime numbers?

Here's a note that calculates it as 1. Do you know of any other calculations? http://www.math-math.com/2014/05/shannon-entropy-shannon-entropy-of.html
4
votes
0answers
43 views

Looking for a a measure-theoretic treatment of “differential entropy”

If $X$ is a discrete random variable, its entropy $H(X)$ is usually defined as something along the lines of $-\sum \def\P{\mathbb{P}}\P(x) \log_2( \P(x))$, where the sum ranges over all the possible ...
3
votes
0answers
107 views

Reference for a transformation

Has the (Lebesgue-)ergodic transformation $T: \{0,1\}^{\mathbb{N}} \to \{0,1\}^{\mathbb{N}}$ defined by $T(x(0)x(1)x(2)\cdots) = x(1)x(3)x(5)\cdots$ been well-studied? If so, where? Does it have a ...
0
votes
1answer
88 views

How to compute Shannon information?

Given a string of random symbols with yet a priori unknown distribution, what are the known algorithms to compute its Shannon entropy? $$H = - \sum_i \; p_i \log p_i$$ Is there an algorithm to ...