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

Copyright © 2019 by Academia Scientiarum Fennica