Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms (Q1842783)

Let \(X\) be a topological space which is the union of increasing subspaces \(K_n\) (\(n=1,2,\dots\)) each of which supports a complete separable metric. It is shown how to construct a configuration space \(\Gamma_X\) with a \(\sigma\)-algebra \(\mathcal C\) of measurable subsets. From a non-atomic Borel measure on \(X\) is constructed a Poisson measure on \((\Gamma_X,{\mathcal C})\). Properties of this measure are studied, including ergodicity, before specializing to the case where \(X\) is a connected, non-compact, metrizable \(C^\infty\)-manifold.