Let us say you have a random variable $R$. How would one generate a uniform random variable $U$, with the maximum possible entropy (or infinite entropy, if $R$ has such)? (For simplicity, you may assume that $R$'s sample space is a subset of the real numbers.)
Note: $U$ is essentially gotten by applying a function to $R$. I believe what I am seeking is called a "randomness extractor", specifically one that preserves entropy, and works based a probability distribution.