2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229658It is shown that for every $α$, where $α\in [0, 1/2]$, there exists an $α$-rigid transformation whose spectrum has Lebesgue component. This answers the question posed by Klemes and Reinhold in [7]. We apply a certain correspondence between weak limits of powers of a transformation and its skew products.3 pagesDynamical SystemsSpectral Theory37Axx, 28D05text