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We consider a special case of the question of classification of invariantRadon measures of $\mathbb{Z}^m$-valued skew-products over interval exchangetransformations, which arise as Poincar\'e sections of the linear flow onperiodic infinite translation surfaces. In the case of periodic typeskew-products, we obtain a full classification of ergodic invariant Radonmeasures, showing them to be precisely the Maharam measures, a family ofmeasures parametrised by $\mathbb{R}^m$. For the proof we translate Rauzy-Veechrenormalisation for skew-products into the symbolic language of the adiccoding, 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 tofind an explicit form for the Maharam measures and deduce the weak*-continuityof the measures depending on the parameter.

Ergodic measures for periodic type $\mathbb{Z}^m$-skew-products over Interval Exchange Transformations