  For Dynkin and Euclidean quivers, it is shown that Gabriel-Roiter measures of
thin representations equal the induced chain length functions on the
corresponding system of subquivers. This allows a combinatorial procedure to
find a GR filtration of thin representations, showing that GR measures of thin
representations are field-independent. It is proved that an indecomposable
filtration of a thin representation is a GR filtration for a suitable choice of
a length function on the category of finite-dimensional representations.
