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Given a random variable $X$ that is uniformly distributed on $[-b,b]$ and $Y=g(X)$ with $$g(x) = \begin{cases} 0, ~~~ x\in [-c,c] \\ x, ~~~ \text{else}\end{cases}$$ Now I want to compute the ...

I'm exploring the possibility to apply information theory on an uncountably infinite-dimensional scenario. I found the concept of generalized entropy for continuous random variables defined on finite-...

Define the (differential) entropy for a density $f$ as $$ H(f) :=-\int_{0}^{1} f(x) \log_{2}(f(x)) dx \, .$$ I am trying to find a $f \in L_{1}([0,1])$ such that $f\geq 0, \int_{0}^{1} f(x) dx = 1$...

Let $G$ be a locally compact group. A measure $\mu$ is the right-Haar measure on $G$ if for every $g\in G$ and $E\subseteq G$ Borel set $\mu(Eg)=\mu(E)$. It is known that every locally compact group ...