Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups

We study the notion of intrinsic Lipschitz graphs within Heisenberg groups, focusing our attention on their Hausdorff dimension and on the almost everywhere existence of (geometrically defined) tangent subgroups. In particular, a Rademacher type theorem enables us to prove that previous definitions of rectifiable sets in Heisenberg groups are natural ones.