Abstract:Abstract. We consider a quadruple (Ω, A , ϑ, μ), where A is a σ-algebra of subsets of Ω, and ϑ is a measurable bijection from Ω into itself that preserves a finite measure μ. For each B ∈ A , we define and study the measure μ B obtained by integrating on B the number of visits to a set of the trajectory of a point of Ω before returning to B. In particular, we obtain a generalization of Kac's formula and discuss its relation to discretetime Palm theory. Although classical in appearance, its use in obtaining uni… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.