Metrically invariant measures on locally homogeneous spaces and hyperspaces
type: Item
instance of: scholarly article
title: Metrically invariant measures on locally homogeneous spaces and hyperspaces
zbMATH Open document ID: 0604.28009
author: Christoph Bandt
author: Gebreselassie Baraki
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: We compare different invariance concepts for a Borel measure \(\mu\) on a metric space. \(\mu\) is called open-invariant if open isometric sets have equal measure, metrically invariant if isometric Borel sets have equal measure, and strongly invariant if any non-expansive image of A has measure \(\leq \mu (A)\). On common hyperspaces of compact and compact convex sets there are no metrically invariant measures. A locally compact metric space is called locally homogeneous if any two points have isometric neighbourhoods, the isometry transforming one point into the other. On such a space there is a unique open-invariant measure, and this measure is even strongly invariant.
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 3975279
zbMATH Keywords: Borel measures on locally compact metric spaces
zbMATH Keywords: locally homogeneous spaces
zbMATH Keywords: Hausdorff measures
zbMATH Keywords: hyperspaces
zbMATH Keywords: metrically invariant measures
MaRDI profile type: Publication
full work available at URL: pjm.1986.121.13
OpenAlex ID: W2037757445
DOI: 10.2140/PJM.1986.121.13
Recommended article: Q4238241
Recommended article: Q4301443
Recommended article: Structure of homogeneous locally compact spaces with intrinsic metric
Recommended article: Invariant measures in quasi-metric spaces
Recommended article: On similarity homogeneous locally compact spaces with intrinsic metric
Recommended article: Measures Invariant under Local Homeomorphisms
Recommended article: Measures that are invariant under transformations of metric compact spaces
Recommended article: Stationary measures and invariant subsets of homogeneous spaces
Recommended article: Homogeneous spaces with inner metric and with integrable invariant distributions
description: scientific article; zbMATH DE number 3975279