  In this article, we prove the existence of measure-valued solutions to the
Ericksen-Leslie system equipped with the Oseen-Frank energy. We introduce the
concept of generalized gradient Young measures. Via a Galerkin approximation,
we show the existence of weak solutions to a regularized system and attain
measure-valued solutions for vanishing regularization. Additionally, it is
shown that the measure-valued solution fulfills an energy inequality.
