Séminaire de Probabilités XLVI pp 401-410
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 (Le Jan, Markov Paths, Loops and Fields, vol. 2026, Springer, Heidelberg, 2011).
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