Let $\{X_n\}_{n=1}^\infty$ be a sequence of random variables defined over a common underlying space $(\Omega, \mathcal F,P)$. We say that $X_n$ converges in probability to a real number $\mu$ iff:
$(\forall \epsilon>0)\lim_{n\rightarrow\infty}P(|X_n-\mu|\geq\epsilon)=0$
I am trying to visualize this in two dimensional graph in $(\Omega, \mathbb R)$. My understading is that as $n$ increases, the probability of the $\omega\in\Omega:|X_n-\mu|\geq\epsilon$ will go to zero. They are highlighted in blue in the Omega axis in the figure below. This means, that the highlighted part will shrink as $n$ increases.
Is this the correct way to visualize convergence in probability to a constant?
