Asymptotics of H-continuous and H-differentiable measures in Hilbert space
type: Item
instance of: scholarly article
title: Asymptotics of H-continuous and H-differentiable measures in Hilbert space
zbMATH Open document ID: 0578.28011
DOI: 10.1007/BF01652514
author: V. A. Romanov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Let H be a Hilbert space with norm \(| \cdot |\), m be a real- valued measure of Borel subsets of H. The paper contains a criterion of the continuity of product-measures (by the definition m is continuous in direction \(h\in H\) if \(var(m_{th}-m)\to 0\quad as\quad t\downarrow 0\); here \(m_ h(A)=m(A+h))\). Asymptotic properties of \(m(| x| <r)\) (as \(r\to 0)\) are also treated.
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 46G12
zbMATH DE Number: 3925181
zbMATH Keywords: differentiable measures
zbMATH Keywords: Hilbert space
zbMATH Keywords: real-valued measure of Borel subsets
zbMATH Keywords: continuity of product-measures
zbMATH Keywords: continuous in direction
zbMATH Keywords: Asymptotic properties
MaRDI profile type: Publication
cites work: Q4127232
cites work: Q5566781
cites work: Q4112159
cites work: Q5642761
full work available at URL: https://doi.org/10.1007/bf01652514
OpenAlex ID: W2016735580
description: scientific article; zbMATH DE number 3925181