On a certain pair of measures on $\ell _p$
On a certain pair of measures on $\ell _p$
A pair of finite Borel measures $\mu$ and $\nu$ on $\ell _p$, $1\le p< \infty$, $\mu \ne \nu$, is constructed so that the identity $\mu (B(x,r))=\nu (B(x,r))$ is fulfilled for all balls $B(x,r)$ with centers $x \in \ell _p$ and radii $r<R(x)$, where $R(x)>0$ for a.e. $x$.