Some results on logarithmic derivatives of measures on a locally convex space
type: Item
instance of: scholarly article
title: Some results on logarithmic derivatives of measures on a locally convex space
zbMATH Open document ID: 0838.46035
DOI: 10.1007/BF01209091
author: N. V. Norin
author: O. G. Smolyanov
published in: Mathematical Notes
publication date: 1995-09-12T00:00:00Z
review text: Let \(\mu\) be a \(\sigma\)-additive real-valued measure on the \(\sigma\)-algebra of Borel subsets of a locally convex linear space \(X\). For \(h\in X\), a real-valued function \(\beta_\mu(h,\cdot)\) is the logarithmic derivative of \(\mu\) in the direction \(h\) if for each real-valued bounded ``smooth'' function on \(X\) holds \[ \int f'(x)h\mu(dx)=- \int f(x) \beta_\mu(h, x)\mu(dx). \] The author studies the problem of restoration of the measure \(\mu\) from its logarithmic derivative.
reviewed by: Hans Weber
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 795658
zbMATH Keywords: problem of restoration of the measure from its logarithmic derivative
zbMATH Keywords: Borel subsets of a locally convex linear space
zbMATH Keywords: logarithmic derivative
MaRDI profile type: Publication
cites work: Q5642761
cites work: On nonlinear transformations of Gaussian measures
cites work: Q3761405
cites work: Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
cites work: MEASURES ON LINEAR TOPOLOGICAL SPACES
full work available at URL: https://doi.org/10.1007/bf01209091
OpenAlex ID: W2032127609
description: scientific article; zbMATH DE number 795658