# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Note on extreme points in Marcinkiewicz function spaces. (English) Zbl 1197.46010
Summary: We show that the unit ball of the subspace ${M}_{W}^{0}$ 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 $\left(0,\infty \right)$ and $W\left(t\right)={\int }_{0}^{t}w$, $t\in \left(0,\infty \right)$. 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 ${f}^{*}=w$.
##### MSC:
 46B20 Geometry and structure of normed linear spaces 46E30 Spaces of measurable functions
##### Keywords:
Marcinkiewicz function spaces; extreme points