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Results tagged with ergodic-theory
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user 2386
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
2
votes
1
answer
766
views
Poincare Recurrence Theorem on Infinite Measure Space
Suppose that $(\Omega,\mathcal{A},\mu)$ is a $\sigma$-finite measure space of infinite measure and $T:\Omega\to\Omega$ a measure-preserving transformation with measurable inverse. Let be $\Omega_k\in …
- 2,044
10
votes
4
answers
2k
views
On The Convergence of Ergodic Measures
I would like to know an example (not using the Gibbs measure Theory) of a sequence of measures $\mu_n:\mathcal B\to[0,1]$ , where $\mathcal B$ is the $\sigma$-algebra of the borelians of a compact spa …
- 2,044
2
votes
1
answer
241
views
Shift Invariance of Backward Martingales for tail trivial probability measures
Consider the infinite cartesian product $\Omega=\{0,1\}^{\mathbb{N}}$
as a measurable space endowed with the $\sigma$-algebra $\mathscr{F}$ generated by the cylinder sets and $\sigma:\Omega\to\Omega$ …
- 2,044
2
votes
0
answers
261
views
A general Lipschtiz potential can be specified by a Gibbs specification ?
I want to consider one-dimensional system on the lattice $\mathbb{L}=\mathbb{N}$.
Let be $A:(\mathbb{S}^1)^{\mathbb{L}}\to\mathbb{R}$ a lipschtiz potential. Consider the Ruelle operator
$$
\mathcal{L …
- 2,044