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Mathematics > Metric Geometry

Title: Differentiation of measures in metric spaces

Abstract: The theory of differentiation of measures originates from works of Besicovitch in the 1940's. His pioneering works, as well as subsequent developments of the theory, rely as fundamental tools on suitable covering properties. The first aim of these notes is to recall nowadays classical results about differentiation of measures in the metric setting together with the covering properties on which they are based. We will then focus on one of these covering properties, called in the present notes the weak Besicovitch covering property, which plays a central role in the characterization of (complete separable) metric spaces where the differentiation theorem holds for every (locally finite Borel regular) measure. We review in the last part of these notes recent results about the validity or non validity of this covering property.
Comments: Lecture Notes of a course given at the CIME-CIRM Course on New Trends on Analysis and Geometry in Metric Spaces, June 26-30, 2017, Levico Terme, Italy
Subjects: Metric Geometry (math.MG); Classical Analysis and ODEs (math.CA)
MSC classes: 28A15
Cite as: arXiv:1802.02069 [math.MG]
  (or arXiv:1802.02069v1 [math.MG] for this version)

Submission history

From: Severine Rigot [view email]
[v1] Tue, 6 Feb 2018 16:56:54 GMT (18kb)