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Borel complexity of the space of probability measures

Authors:	Abhijit Dasgupta

Abstract:	Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if is any non-Polish Borel subspace of a Polish space, then , the space of probability Borel measures on with the weak topology, is always true ${\boldsymbol{\Pi}^{\boldsymbol{0}}_{\boldsymbol{\xi}}}$ , where $\xi$ is the least ordinal such that is ${\boldsymbol{\Pi}^{\boldsymbol{0}}_{\boldsymbol{\xi}}}$ .

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