Multi-occupation field generates the Borel-sigma-field of loops

In this article, we consider the space of càdlàg loops on a Polish space $S$. The loop space can be equipped with a ``Skorokhod'' metric. Moreover, it is Polish under this metric. Our main result is to prove that the Borel-$σ$-field on the space of loops is generated by a class of loop functionals: the multi-occupation field. This result generalizes the result in the discrete case, see \cite{loop}.

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