I have been reading an article and I stumbled upon something that I simply can't work out. Here is a part of the paper: "We denote the probability with respect to $X_n$ by $P_n$, and the expectation with respect to $X_1, ... , X_{n−1} $ by $E_{1,...,n-1}$". Then the authors proceed to conclude something that boils down to $P[(X_1, ... , X_n) \in A]$ <= $E_{1,...,n-1}$ $P_n[(X_1, ... , X_n) \in A]$. Can someone please help me understand how is this true? I would appreciate any help.
I am linking the paper in case someone would like to take a look: https://arxiv.org/pdf/math/0703503.pdf . It's on page 19, inequality (3.10)