All Questions
8 questions
13
votes
1
answer
559
views
Entropy of composition
I asked this at math.stackexchange.com, but got no answers.
Let $(X,B,\mu)$ be a probability space. Let $T,S:X→X$ be two measurable measure preserving maps that commute (i.e $TS=ST$). Let $A$ be a (...
- 133
2
votes
1
answer
267
views
entropy and d-bar: how do we estimate continuity?
Let $G = \{0,1\}^{\mathbb{N}} = \mathbb{Z}_{2}^{\mathbb{N}}$ be the Bernoulli space of two symbols, let $\sigma$ be the shift map and $M(G)$ the set of $\sigma$-invariant probabilities. Let $\bar{d}$ ...
1
vote
1
answer
410
views
joining or coupling
given two shift invariant measures in the Bernoulli space $\{0,1\}^{\mathbb{N}}$, is there a way to construct joinings of them? It's very diffcult, in general, to find exactly the minimal joining i.e, ...
1
vote
1
answer
182
views
Friedland metric entropy
I was asking if it is possible to extend the definition of topological Friedland entropy for $\mathbb{Z}^d$ continuos actions to measure preserving actions.
The topologica Friedland entropy is ...
- 121
1
vote
1
answer
213
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the "observable" space of a measure space [closed]
For a measure space $(X,\mathcal{A},\mu)$, the space of "observables" with respect to finite set $F$ which is endowed with counting measure on all of its subsets, is defined as follows:
$$obs (X, \mu,...
- 181
1
vote
1
answer
372
views
Entropy, Convergence
imagine you have a sequence $\eta_{n}$ of (shift) invariant measures in the Bernoulli space $\{0,1\}^{\mathbb{N}}$ that satisfy the following: there are a $0<\delta <1$ and an $N$ such that $$n &...
1
vote
0
answers
139
views
weak-* versus entropy growth
General question. Let $\eta_{n}$ be a sequence of invariant measures on $\{0,1,2,...,p-1\}^{\mathbb{N}}$ and $B$ the Bernoulli uniform measure. Knowing that $\eta_{n} \rightarrow B$ in the weak-* ...
0
votes
1
answer
172
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entropy growth of invariant measures - General question
In general, given a sequence of shift-invariant measures $\eta_{n}$ on $\{0,1\}^{\mathbb{N}}$ what to do to guarantee this convergence of entropies: $$h(\eta_{n}) \rightarrow \log2?$$
Because I'm ...