On quasi-invariant measures in topological vector spaces
type: Item
instance of: scholarly article
title: On quasi-invariant measures in topological vector spaces
zbMATH Open document ID: 0935.46047
author: H. Hogbe Nlend
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1999-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/120217
review text: On an infinite-dimensional locally convex topological vector space \(X\) over \(\mathbb{R}\) there exists no \(\sigma\)-finite Borel measure which is quasi-invariant with respect to translations by the elements of \(X\). This theorem was proved by \textit{V. N. Sudakov} [Dokl. Akad. Nauk SSSR 127, 524-525 (1959; Zbl 0100.11001)], and some special case is discussed in Chap. IV, Sect. 5, of \textit{I. M. Gel'fand} and \textit{N. Ya. Vilenkin} [`` Applications of Harmonic Analysis'', Academic Press (1964; Zbl 0136.11201)]. Another proof was also given by \textit{Y. Umemura} [Publ. Res. Inst. Math. Sci., Kyoto Univ., Ser. A 1, 1-47 (1965; Zbl 0181.41502)]. The note under review concerns this theorem.
reviewed by: Takashi Ichinose
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 1266842
zbMATH Keywords: quasi-invariant measure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1266842