In this talk I will present some recent construction of Tommaso de Fernex and Chung Ching Lau of a measure on the Berkovich space of a complex scheme, which can be viewed as a hybrid between the motivic and the Lebesgue measure. I will first give a short introduction to the theory of motivic integration using the story of K-equivalent varieties to highlight the usefulness of the construction. I will then give a brief description of the construction of Fernex and Lau explaining the similarities and differences between this construction and the classical theory.