Rank as a function of measure
  We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing sequence of upper semicontinuous functions) 
Tomasz Downarowicz, Yonatan Gutman and Dawid Huczek
math.DS