In this exercise 8.M I have already shown that the collection of sets given forms an $\sigma$-algebra and that $ \lambda, \mu $ are measures and that $\lambda \ll \mu$. I could not show that the Radón-nikodým theorem fails, but I think that perhaps with a contradiction argument assuming the existence of f satisfying the Radón-nikodým theorem and finding a suitable set can solve the problem. But I could not define such a set. Any suggestion?