I will start by surveying on the Möbius disjointness conjecture of P.Sarnak, which was introduced in 2010 and has initiated many studies.
Then, I will discuss a result of J. Bourgain, which establishes the conjecture for a class of three-interval exchange maps.
I will present a result, where we estimate the measure of the parameter set in his result. As a consequence, we will show that it has positive, but not full Hausdorff dimension.