Geodesic
On~measures with the doubling condition
Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 629-638

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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. 
@article{IM2_1988_30_3_a9,
     author = {A. L. Vol'berg and S. V. Konyagin},
     title = {On~measures with the doubling condition},
     journal = {Izvestiya. Mathematics },
     pages = {629--638},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a9/}
}
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A. L. Vol'berg; S. V. Konyagin. On~measures with the doubling condition. Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 629-638. http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a9/