Extreme points of the set of elements majorised by an integrable function: Resolution of a problem by Luxemburg and of its noncommutative counterpart

D. Dauitbek, J. Huang, F. Sukochev

Let $f$ be an arbitrary integrable function on a finite measure space $(X,\Sigma ,\nu )$. We characterise the extreme points of the set $\Omega (f)$ of all measurable functions on $(X,\Sigma ,\nu )$ maj…