an:05702395 Zbl 1197.46010 Kami\'nska, Anna; Parrish, Anca M. Note on extreme points in Marcinkiewicz function spaces. EN Banach J. Math. Anal. 4, No. 1, 1-12, electronic only (2010). ISSN 1735-8787/e 2010

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*46B20 46E30 Marcinkiewicz function spaces; extreme points Summary: We show that the unit ball of the subspace $M^0_W$ of order 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 $W(t)=\int^t_0 w$, $t \in (0,\infty)$. 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 $f^*=w$.