\begin{definition}[Definition:Convergence in Probability]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $\sequence {X_n}_{n \mathop \in \N}$ be a sequence of real-valued random variables on $\struct {\Omega, \Sigma, \Pr}$.
Let $X$ be a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$. 
We say that $\sequence {X_n}_{n \mathop \in \N}$ '''converges in probability''' to $X$ {{iff}}: 
:$\ds \forall \epsilon \in \R_{>0}: \lim_{n \mathop \to \infty} \map \Pr {\size {X_n - X} < \epsilon} = 1$
This is written: 
:$X_n \xrightarrow p X$
\end{definition}