1 Borel sets
2 Borel probability measure
3 Weak convergence of measures
4 The Prohkorov metic
Let be a metric space. Denoted by all the Borel probability measure on .
We have defined the notation of weak convergence in , Define for
The function is called the Prokhorov metric on (induced by ).
Conclusion If is a separable metric space, then so is with the induced Prokhorov metric. Moreover, a sequence in converges in metric if and only if it converges weakly and to the same limit.