Academic Journal
The (sub/super)additivity assertion of Choquet
| Τίτλος: | The (sub/super)additivity assertion of Choquet |
|---|---|
| Συγγραφείς: | Heinz König |
| Πηγή: | Measure and Integration ISBN: 9783034803816 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Institute of Mathematics, Polish Academy of Sciences, 2003. |
| Έτος έκδοσης: | 2003 |
| Θεματικοί όροι: | convex functions, Riesz representation, Measures and integration on abstract linear spaces, (sub/super)modular functionals, 02 engineering and technology, Set functions and measures on topological spaces (regularity of measures, etc.), Stonean function classes, 01 natural sciences, Stonean and truncable functionals, (sub/super)additive functionals, Danull-Stone representation, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, 0202 electrical engineering, electronic engineering, information engineering, Choquet integral, Contents, measures, outer measures, capacities, 0101 mathematics, Integration with respect to measures and other set functions |
| Περιγραφή: | Summary: The assertion in question comes from the short final section in ``Theory of capacities'' of \textit{G. Choquet} [Ann. Inst. Fourier 5, 131-295 (1953/54; Zbl 0064.35101)], in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper context and scope of the assertion has remained open. In this paper we present a counterexample which shows that the initial context has to be modified, and then in a new context we prove a comprehensive theorem which fulfils all the needs that have turned up so far. |
| Τύπος εγγράφου: | Article Part of book or chapter of book |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1730-6337 0039-3223 |
| DOI: | 10.4064/sm157-2-4 |
| DOI: | 10.1007/978-3-0348-0382-3_12 |
| DOI: | 10.22028/d291-26236 |
| Σύνδεσμος πρόσβασης: | https://www.impan.pl/shop/publication/transaction/download/product/89574?download.pdf http://www.math.uni-sb.de/service/preprints/preprint84.pdf https://zbmath.org/1927670 https://doi.org/10.4064/sm157-2-4 https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/157/2/89574/the-sub-super-additivity-assertion-of-choquet http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-4 http://journals.impan.pl/cgi-bin/doi?sm157-2-4 https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/26292 https://rd.springer.com/chapter/10.1007/978-3-0348-0382-3_12 https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/26292/1/preprint_84_03.pdf |
| Rights: | Springer TDM |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....4c5c60b0c2fd7dacd9f4dbd66f66aabd |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 17306337 00393223 |
|---|---|
| DOI: | 10.4064/sm157-2-4 |