A reduction technique for limit theorems in analysis and probability theory
type: Item
instance of: scholarly article
title: A reduction technique for limit theorems in analysis and probability theory
zbMATH Open document ID: 0757.28006
DOI: 10.1007/BF02384860
author: Peter A. Loeb
author: Jürgen Bliedtner
published in: Arkiv för Matematik
publication date: 1993-01-16T00:00:00Z
review text: The main result of the present paper, strengthening an earlier result of the authors [Arch. Math. 43, 373-376 (1984; Zbl 0603.31009)], essentially says that (under suitable assumptions) for each measure \(\mu\) in a given class \(M_ 0\) and for some reference measure \(\sigma\), the Radon- Nikodým derivative \(d\mu/d\sigma\) is equal to a limit along a directed set \(I\) of ratios \(R_ i(\mu,\sigma)\), \(i\in I\) (depending on \(\mu\) and \(\sigma)\) \(\sigma\)-almost everywhere. The authors obtain two conditions each of which being equivalent to the just mentioned property. They give interesting applications of their main result, including boundary limit theorems in potential theory, martingale limit theory and density theorems in measure theory.
reviewed by: Klaus Schürger
Mathematics Subject Classification ID: 28A15
Mathematics Subject Classification ID: 31C40
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 91589
zbMATH Keywords: Radon-Nikodým derivative
zbMATH Keywords: boundary limit theorems in potential theory
zbMATH Keywords: martingale limit theory
zbMATH Keywords: density theorems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 91589