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Note on extreme points in Marcinkiewicz function spaces. (English) Zbl 1197.46010
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 $f^*=w$.

46B20Geometry and structure of normed linear spaces
46E30Spaces of measurable functions
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