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A Metric Space is called Polish if it is Separable and complete.
and are examples of Polish spaces.
- Precompactness can be defined using either Relatively Compact or Totally Bounded - Allows for Prokhorov’s Theorem to work both ways - being polish means is polish. - Presumably makes the process showing a space is Metrizable easier. - Avoids many pathologies in probability theory.
Weak convergence
Wasserstein metric
Weak convergence in Wasserstein space
Wasserstein distance metrizes Wasserstein space
Controlled Markov Chain
Markov Decision Process
Blackwell's Irrelevant Information Theorem
Partially Observable Markov Decision Process
Prokhorov's Theorem
Feller condition for invariant measure
Precompact
Showing F_m is closed