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We provide a thorough description of the free boundary for the lowerdimensional obstacle problem in $\mathbb{R}^{n+1}$ up to sets of null$\mathcal{H}^{n-1}$ measure. In particular, we prove (i) local finiteness ofthe $(n-1)$-dimensional Hausdorff measure of the free boundary, (ii)$\mathcal{H}^{n-1}$-rectifiability of the free boundary, (iii) classificationof the frequencies up to a set of dimension at most (n-2) and classification ofthe blow-ups at $\mathcal{H}^{n-1}$ almost every free boundary point.

On the measure and the structure of the free boundary of the lower dimensional obstacle problem