A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $

Abstract

In this note, we derive an equation which describes the closure of a particular set comprising $n-$valued functions. This result provides an answer to a long standing question for which the particular case $n=2$ had been known and used frequently in the optimal control problems.

Keywords

• $n-$valued functions
• formulation
• weak$^\star $ closure
• rearrangements
• eigenvalues