# American Institute of Mathematical Sciences

July  2014, 34(7): 2741-2750. doi: 10.3934/dcds.2014.34.2741

## Rank as a function of measure

 1 Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wroc law, Poland, Poland 2 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland

Received  June 2012 Revised  October 2013 Published  December 2013

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).
Citation: Tomasz Downarowicz, Yonatan Gutman, Dawid Huczek. Rank as a function of measure. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2741-2750. doi: 10.3934/dcds.2014.34.2741
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