Note on extreme points in Marcinkiewicz function spaces

Abstract

We show that the unit ball of the subspace $M_W^0$ of ordered continuous elements of $M_W$ has no extreme points, where $M_W$ is the Marcinkiewicz function space generated by a decreasing weight function $w$ over the interval $(0,\infty)$ and $W(t) = \int_0^tw$, $t\in(0,\infty)$. We also present here a proof of the fact that a function $f$ in the unit ball of $M_W$ is an extreme point if and only if $f^*=w$.