In this thesis we will use indecomposable representations of the 3-Kronecker quiver to construct uncountably many infinite Gabriel-Roiter measures. Our aim is to classify all piling submodules of an indecomposable regular module. We will show that they are either unique of a certain length or there is a one-parameter family of such submodules. A possible largest Gabriel-Roiter measure in the central part is discussed.