I was curious about the paper A New Outlook on Shannon’s Information Measures by Yeung. However, I don't really understand the abstract
Let. $X_i,i = 1,. . .,n$, be discrete random variables, and $\tilde{X}_i$ be a set variable corresponding to $X_i$. Define the universal set to be $\bigcup_{i=1}^n\tilde{X}_i$ and let $S$ be the $\sigma$-field generated by $\{\tilde{X}_i,i = 1,. . . ,n\}$
what does
$\tilde{X}_i$ be a set variable corresponding to $X_i$
mean?
and what is the $\sigma$-field generated by $\{\tilde{X}_i,i = 1,. . . ,n\}$?