Let us call $\Lambda$ homogeneous if there is an $\epsilon>0$ so that for all $r>0$ and $x,y$ in the support of $\Lambda$, we have

$$\Lambda(B(x,r))>\epsilon\Lambda(B(y,r))$$

where as usual $B(x,r)$ is the ball of radius $r$ centred at $x$. I am thinking of $\mathbb{R}^d$ but it could be a general metric space. Q: Is this (equivalent to) a known definition in the literature?