With a view to generalising rectifiability and density results to more general spaces we prove the following: let $H^s$ denote Hausdorff $s$ measure in $l^n_{\infty}$. Let $s\in(0,2]$. Let $S\subset l^n_{\infty}$ be a subset of positive locally finite Hausdorff $s$-measure with the property $$\lim_{r\rightarrow 0} \frac{H^s(B_r(x)\cap S)}{\alpha(s)2^{-s}r^s}=1\;\;\;\mathrm{for}\;\;H^{s}\;a.e.\;x\in S,$$ then $s$ is an integer and $S$ has a weak tangent at almost every point.