Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 1015-1030

THE LEAST DOUBLING CONSTANT OF A METRIC MEASURE SPACE

Javier Soria and Pedro Tradacete

University of Barcelona, Department of Mathematics and Computer Science
Gran Via 585, E-08007 Barcelona, Spain; soria 'at' ub.edu

Consejo Superior de Investigaciones Científicas, Instituto de Ciencias Matemáticas
Campus de Cantoblanco UAM, 28049 Madrid, Spain; pedro.tradacete 'at' icmat.es

Abstract. We study the least doubling constant C_(X,d), among all doubling measures μ supported on a metric space (X,d). In particular, we prove that for every metric space with more than one point, C_(X,d) ≥ 2. We also describe some further properties of C_(X,d) and compute its value for several important examples.

2010 Mathematics Subject Classification: Primary 54E35, 28C15.

Key words: Metric spaces, doubling measures.

Reference to this article: J. Soria and P. Tradacete: The least doubling constant of a metric measure space. Ann. Acad. Sci. Fenn. Math. 44 (2019), 1015-1030.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4457