Unbounded mappings and weak convergence of measures

August Michal Zapala

Statistics & Probability Letters, 2008, vol. 78, issue 6, 698-706

Abstract: Weak convergence of finite Borel measures in a completely regular topological space X is defined by means of the class of bounded and continuous functions f:X-->R. We give conditions equivalent to weak convergence of finite measures in terms of some classes of unbounded, continuous and semicontinuous real-valued functions on X. For this purpose we introduce the notion of almost uniformly integrable mappings with respect to a directed family of measures. The obtained results may be treated as an extension of the Alexandroff theorem, also known as portmanteau theorem.

Keywords: Weak; convergence; of; bounded; measures; Lower; (upper); semicontinuous; function; Almost; (asymptotic); uniform; integrability; Completely; regular; topological; space (search for similar items in EconPapers)
Date: 2008
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