$\lim_{n \to \infty} P(|\hat{\theta}_n - \theta| > \epsilon) = 0$ for all $\epsilon > 0$.

$\lim_{n \to \infty} E[\hat{\theta}_n] = \theta$.

$\lim_{n \to \infty} Var(\hat{\theta}_n) = 0$.

$\hat{\theta}_n$ is the Maximum Likelihood Estimator for all $n$.