A note on functions which separate Gaussian measures
type: Item
instance of: scholarly article
title: A note on functions which separate Gaussian measures
zbMATH Open document ID: 0647.60010
DOI: 10.1007/BF01162002
author: Maciej Lewandowski
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174042
review text: Assume that for any measurable function f and two Gaussian measures \(\mu\), \(\nu\) on Banach space E we have \[ \int f(x+y)\mu (dy)=\int f(x+y)\nu (dy)\quad for\quad every\quad x\in E. \] We give a sufficient condition on f which implies that \(\mu\) is a translation of \(\nu\). As a corollary we get that if a bounded function f has bounded support with non-empty interior then \(\mu =\nu\).
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 4056653
zbMATH Keywords: Gaussian measures
zbMATH Keywords: Banach space
zbMATH Keywords: translated functions
MaRDI profile type: Publication
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OpenAlex ID: W1983510861
description: scientific article; zbMATH DE number 4056653