On the existence of doubling measures with certain regularity properties

1998/04/14 by Per Bylund, Bylund, Per, Jaume Gudayol +1
Mathematics · #54F45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 28C15 #Secondary 54E45 #math.CA #msc:28C15 #msc:54E45 #msc:54F45

paper · pdf · doi:10.48550/arxiv.math/9804070

LaTeX2e file, 16 pages

arxiv created 1998/04/14 · arxiv updated 2009/11/30

Abstract

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.

Related

• The doubling metric and doubling measures
• The least doubling constant of a metric measure space
• Minimizing measures for the doubling condition
• The proof of A₂ conjecture in a geometrically doubling metric space
• Recovering measures from approximate values on balls