Connection between the Riemann integrability of a multi-valued function and of its convex hull
| Autor: | Olha Shevchenko, Vladimir Kadets, Artur Kulykov |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Convex hull
Mathematics::Functional Analysis Pure mathematics 46B20 28B20 Applied Mathematics Banach space Function (mathematics) Computer Science::Computational Geometry Functional Analysis (math.FA) Mathematics - Functional Analysis Riemann hypothesis symbols.namesake Bounded function Norm (mathematics) FOS: Mathematics symbols Mathematics::Metric Geometry Connection (algebraic framework) Equivalence (measure theory) Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 505:125652 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2021.125652 |
| Popis: | For a Banach space X we demonstrate the equivalence of the following two properties: (1) X is B-convex (that is, possesses a nontrivial infratype), and (2) if F : [ 0 , 1 ] → 2 X ∖ { ∅ } is a multifunction with bounded values, convF denotes the multifunction t ↦ conv ( F ( t ) ) , then the Riemann integrability of convF is equivalent to the Riemann integrability of F. For multifunctions with relatively norm compact values the Riemann integrability of convF is equivalent to the Riemann integrability of F without any restrictions on the Banach space X. |
| Databáze: | OpenAIRE |
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