This article is cited in 42 papers

On measures with the doubling condition

A. L. Vol'berg, S. V. Konyagin


Abstract: The author characterizes metric spaces $(X,\rho)$ that carry a nontrivial measure $\mu$ with the doubling condition
$$ \forall\,x\in X,\quad R>0\qquad \mu(B(x,2R))\leqslant C\mu(B(x,R)), $$
where $B(x,R)=\{y:\rho(x,y)\leqslant R\}$. In particular, such a measure exists on any compact set in $\mathbf R^n$.
Bibliography: 14 titles.

UDC: 519.53

MSC: Primary 28C15; Secondary 54E53, 54E45

Received: 07.05.1985

 English version: Mathematics of the USSR-Izvestiya, 1988, 30:3, 629–638

Bibliographic databases:

• 
• 
•