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Polish space

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Definition
StochasticControl

A Metric Space is called Polish if it is Separable and complete.

R\mathbb{R} and [0,1][0,1] 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 - X\mathbb{X} being polish means P(X)\mathcal{P}(\mathbb{X}) is polish. - Presumably makes the process showing a space is Metrizable easier. - Avoids many pathologies in probability theory.

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