Some calculations on the conditional densities of well-admissible measures on linear spaces
type: Item
instance of: scholarly article
title: Some calculations on the conditional densities of well-admissible measures on linear spaces
zbMATH Open document ID: 0796.31007
DOI: 10.1007/BF01047843
author: Shiqi Song
published in: Potential Analysis
publication date: 1994-10-05T00:00:00Z
review text: The paper deals with so-called well-admissible measures on a topological vector space \(E\). The notion of well-admissibility was first introduced in [\textit{S. Albeverio}, \textit{S. Kusuoka} and \textit{M. Röckner}, J. Lond. Math. Soc. 42, 122-136 (1990; Zbl 0667.31010)] and has applications to many models of Dirichlet forms; however its definition is too long to be given here. It is known that when a probability measure on \(E\) is well- admissible in a direction \(k \in E\), the conditional law in the direction \(k\) given the other directions is absolutely continuous with respect to the Lebesgue measure. The author proves that its density function is differentiable and calculates its derivatives. The results are applied to compute the capacity of the zero set of the conditional density function, and sufficient conditions are obtained ensuring that the space of bounded smooth functions is dense in a Dirichlet space.
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 46G12
zbMATH DE Number: 554339
zbMATH Keywords: well-admissible measures
zbMATH Keywords: topological vector space
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: capacity
zbMATH Keywords: zero set of the conditional density function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 554339