# Tagged Questions

**9**

votes

**1**answer

202 views

### Entropy for Haar measure on $O(n)$

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 ...

**2**

votes

**2**answers

246 views

### probability measures with entropy equal to nonnegative number

Is it true that for a given nonnegative number, there exists a measure-theoretical entropy value (supremum of entropies of all partitions under a measure-preserving transformation) that equals this ...

**1**

vote

**1**answer

359 views

### existence of finitely additive measures with zero entropy

Let $X$ be a countable set and $\mathcal M(X)$ be the set of finitely additive probability measures on $X$. If $\mu\in\mathcal M(X)$, I define the entropy of $\mu$ to be
$$
...