Browsing by Author "Laurain, Paul"

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    CLASSIFICATION OF UNIFORMLY DISTRIBUTED MEASURES OF DIMENSION 1 IN GENERAL CODIMENSION
    (2021) Laurain, Paul; Petrache, Mircea
    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.