CLASSIFICATION OF UNIFORMLY DISTRIBUTED MEASURES OF DIMENSION 1 IN GENERAL CODIMENSION
No Thumbnail Available
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in R-d has remained open, except. for d = 1 and for compactly supported measures in d = 2, and for codimension 1. In this paper we study 1-dimensional measures in R-d for all d and classify uniform measures with connected 1-dimensional support, which turn out to be homogeneous measures. We provide as well a partial classification of general uniform measures of dimension 1 in the absence of the connected support hypothesis.
Description
Keywords
uniform measures, homogeneous measures, helices, higher codimension