Recent content by fsblajinha

$\Omega = \{0,1\}^{\mathbb{Z}^{2}}$ is the set of open and closed $\mathbb{Z}^{2}$ $\Omega_{\wedge} = \{0,1\}^{\wedge}, \forall \wedge \subset \mathbb{Z^{2}}$ finite. $C:=$Cylinders (That is, local events that depend on a finite number of sites); $\Pi_{\wedge}:\Omega \rightarrow...

I can not prove that it has empty interior! Thank you!

In $\Omega = \{0,1\}^{\mathbb{Z}^{2}}$, consider the class $C$ of cylinders. Show that $C$ is algebra. At $w\in \Omega$, we call cluster point $x$ all points $z\in \mathbb{Z}^{2}$ that can be attained from $x$ by a path that only passes by open dots. In the $\sigma$-algebra generated by $C...

Is $q_ {1} q_ {2}, ...,$ an enumeration of the rational $[0,1]$. For every $\epsilon> 0$, let $\displaystyle{A _ {\epsilon}: = [0,1]-\bigcup_ {n \geq 1} I_{n}}$, where $I_{n}:= [q_{n} - \frac {\epsilon}{2^{n+1}} , q_{n}\frac{\epsilon}{2^{n + 1}}]\cap [0,1]$. Show that: 1 - $A _ {\epsilon}$ is...