Suppose X is a random variable taking values in a complete separable metric space. If ε > 0, show there exists a compact set K such that   Suppose X n converges weakly to X and the metric space S is...

Suppose X is a random variable taking values in a complete separable metric space. If ε > 0, show there exists a compact set K such that

Suppose X_n
converges weakly to X and the metric space S is complete and separable. Prove that the sequence {X_n} is tight.

Suppose S is a separable metric space. Show that M is separable.

Chapter 31