I will try to explain the fundamental strategy of Katok-Spatzier for higher-rank measure rigidity, highlighting the crucial role played by leafwise measures.

Then we will state the recent measure rigidity theorem of Einsiedler-Lindenstrauss and try to provide an overview of the proof, indicating the steps and the constructions which will be presented later in the seminar. The talk should be (essentially) accessible and independent from the previous talk by Ralf.