FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2080644971> ?p ?o ?g. }

• W2080644971 endingPage "1019" @default.
• W2080644971 startingPage "1013" @default.
• W2080644971 abstract "IN THE last several years, in order to avoid convexity assumptions, an effort has been produced to find classes of sets that inherit some of the properties of convex sets from less geometric and more analytic considerations. The theory of decomposable sets is the product of such an effort. A decomposable set D is a subset of L’ = L’( T, E), where T is a measure space and E a Banach space, having the property that UXA + UXT_A E D for every U, u E D and for every measurable subset A of T. One can find in [l-4] results in which decomposability is in some sense a substitute of convexity. As it turned out a decomposable, closed and bounded set is the set of measurable selections of an integrably bounded multifunction (that could describe the constraint of the problem), i.e. dealing with a bounded decomposable set, we actually deal with a set of functions pointwise, a.e. bounded by some functions in L’. This last limitation is not always met in actual problems: some of the areas’ sources of examples lead to consider bounds coming from growth conditions or coercivity conditions: typical cases arise in the calculus of variations or, more generally, in the investigation of variational problems. In such problems one meets so-called sublevel sets which in general can be defined as sets of functions u E L' such that S @ 0 ]]u]] is bounded by a constant M, possibly infinite, where the function @: [0, co[ + [0, oo[ has the only property that Q 0 II 11 u is measurable for any u E L'. Since the assumptions on @ are very weak, the class of sublevels contains a certain amount of subsets of L', such as Orlicz classes, LP-spaces (0 < p < co), balls in such spaces, and so on. However these sets, denoted by QM, are not decomposable and the purpose of this note is to extend the theory developed for decomposable sets to sets of the type QM fl D, i.e. to sets which are the intersection of a sublevel and of a set of selections of a measurable multifunction (but not necessarily bounded). In this way we cover the case of a weakly relatively compact family of functions in L', taking values in a closed subset M of E assuming neither the boundedness of It4 nor the existence of an integral bound for the family itself, as would be required within the framework of decomposable sets. It should be remarked that &, of D can be chosen to be the whole space, including, as a particular case, the theory for decomposable sets and for sublevels. We present a metric and a topological result: first we prove that the Kuratowski index (Y of a set of the type specified above, coincides with its diameter, then we give a version of the Dugundji extenstion theorem. In [2] the authors give an extension theorem in which decomposability in L' is used instead of convexity in a generic Banach space, obtaining, as a consequence, that a closed decomposable set in a separable space L' is a retract, and that, in general, it has the compact fixed point property. We prove analogous statement for our case." @default.
• W2080644971 created "2016-06-24" @default.
• W2080644971 creator A5087274494 @default.
• W2080644971 date "1993-04-01" @default.
• W2080644971 modified "2023-09-30" @default.
• W2080644971 title "Metric and topological properties of nondecomposable sets" @default.
• W2080644971 cites W107401925 @default.
• W2080644971 cites W1527244075 @default.
• W2080644971 cites W1561653341 @default.
• W2080644971 cites W1563933852 @default.
• W2080644971 cites W2062933775 @default.
• W2080644971 cites W2145705229 @default.
• W2080644971 cites W2299856668 @default.
• W2080644971 cites W984468693 @default.
• W2080644971 doi "https://doi.org/10.1016/0362-546x(93)90091-6" @default.
• W2080644971 hasPublicationYear "1993" @default.
• W2080644971 type Work @default.
• W2080644971 sameAs 2080644971 @default.
• W2080644971 citedByCount "0" @default.
• W2080644971 crossrefType "journal-article" @default.
• W2080644971 hasAuthorship W2080644971A5087274494 @default.
• W2080644971 hasConcept C114614502 @default.
• W2080644971 hasConcept C144133560 @default.
• W2080644971 hasConcept C162853370 @default.
• W2080644971 hasConcept C176217482 @default.
• W2080644971 hasConcept C184720557 @default.
• W2080644971 hasConcept C202444582 @default.
• W2080644971 hasConcept C33923547 @default.
• W2080644971 hasConcept C81332173 @default.
• W2080644971 hasConceptScore W2080644971C114614502 @default.
• W2080644971 hasConceptScore W2080644971C144133560 @default.
• W2080644971 hasConceptScore W2080644971C162853370 @default.
• W2080644971 hasConceptScore W2080644971C176217482 @default.
• W2080644971 hasConceptScore W2080644971C184720557 @default.
• W2080644971 hasConceptScore W2080644971C202444582 @default.
• W2080644971 hasConceptScore W2080644971C33923547 @default.
• W2080644971 hasConceptScore W2080644971C81332173 @default.
• W2080644971 hasIssue "8" @default.
• W2080644971 hasLocation W20806449711 @default.
• W2080644971 hasOpenAccess W2080644971 @default.
• W2080644971 hasPrimaryLocation W20806449711 @default.
• W2080644971 hasRelatedWork W2047417452 @default.
• W2080644971 hasRelatedWork W228803548 @default.
• W2080644971 hasRelatedWork W2369307287 @default.
• W2080644971 hasRelatedWork W2586442026 @default.
• W2080644971 hasRelatedWork W2725985693 @default.
• W2080644971 hasRelatedWork W2772484191 @default.
• W2080644971 hasRelatedWork W2804682772 @default.
• W2080644971 hasRelatedWork W3173101182 @default.
• W2080644971 hasRelatedWork W4281784891 @default.
• W2080644971 hasRelatedWork W3103674034 @default.
• W2080644971 hasVolume "20" @default.
• W2080644971 isParatext "false" @default.
• W2080644971 isRetracted "false" @default.
• W2080644971 magId "2080644971" @default.
• W2080644971 workType "article" @default.