  We consider a special case of the question of classification of invariant
Radon measures of $\mathbb{Z}^m$-valued skew-products over interval exchange
transformations, which arise as Poincar\'e sections of the linear flow on
periodic infinite translation surfaces. In the case of periodic type
skew-products, we obtain a full classification of ergodic invariant Radon
measures, showing them to be precisely the Maharam measures, a family of
measures parametrised by $\mathbb{R}^m$. For the proof we translate Rauzy-Veech
renormalisation for skew-products into the symbolic language of the adic
coding, and apply a symbolic result of Aaronson, Nakada, Sarig and Solomyak.
Further, we use this language and a new extension of the Rauzy-Veech cocycle to
find an explicit form for the Maharam measures and deduce the weak*-continuity
of the measures depending on the parameter.
