Let $X$ be an $n-$dim Alexandrov space with curvature $\geq k$. Does $X$ satisfy a reverse doubling condition? That is, does there exist a constant $C>1$, s.t., for any $x\in X$, $r>0$, $\mathrm{vol}(B_x(2r))\geq C\cdot\mathrm{vol}(B_x(r))$?

Let $X$ be an $n-$dim Alexandrov space with curvature $\geq k$. Does $X$ satisfy a reverse doubling condition? That is, does there exist a constant $C>1$, s.t., for any $x\in X$, $0<r<\mathrm{diam}(X)/2$, $\mathrm{vol}(B_x(2r))\geq C\cdot\mathrm{vol}(B_x(r))$?

Let $X$ be an $n-$dim Alenandrov space with curvature $\geq k$. Does $X$ satisfies a reverse doubling condition  ? That is, does there exists a constant $C>1$, s.t., for any $x\in X$, $r>0$, $\mathrm{vol}(B_x(2r))\geq C\cdot\mathrm{vol}(B_x(r))$?

Let $X$ be an $n-$dim Alexandrov space with curvature $\geq k$. Does $X$ satisfy a reverse doubling condition? That is, does there exist a constant $C>1$, s.t., for any $x\in X$, $r>0$, $\mathrm{vol}(B_x(2r))\geq C\cdot\mathrm{vol}(B_x(r))$?