Choquet type L1-spaces of a vector capacity
Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Submitted version |
| Publication date: | 2017 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103812 |
| Online Access: | https://hdl.handle.net/11441/103812 https://doi.org/10.1016/j.fss.2017.05.014 |
| Access Level: | Open access |
| Keyword: | Non-additive measures Measures of information Choquet integral Fuzzy measure |
| _version_ | 1878734942260690944 |
|---|---|
| author | Delgado Garrido, Olvido |
| author2 | Sánchez Pérez, E. A. |
| author2_role | author |
| author_browse | Delgado Garrido, Olvido Sánchez Pérez, E. A. |
| author_facet | Delgado Garrido, Olvido Sánchez Pérez, E. A. |
| author_role | author |
| collection | idUS. Depósito de Investigación de la Universidad de Sevilla |
| description | Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal necessary conditions on Λ are required, several -spaces of integrable functions associated to Λ appear in such a way that the integration map can be defined in them. We study the properties of these spaces and how they are related. We show that the behavior of the -spaces and the integration map can be improved in the case when X is an order continuous Banach lattice, providing new tools for (non-linear) operator theory and information sciences. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_72e4ff1a52eb12f2d82ca92ee3bec4bb |
| institution | Universidad de Sevilla (US) |
| instname_str | Universidad de Sevilla (US) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:idus.us.es:11441/103812 |
| publishDate | 2017 |
| publishDateSort | 2017 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | idUS. Depósito de Investigación de la Universidad de Sevilla |
| spelling | Choquet type L1-spaces of a vector capacity Delgado Garrido, Olvido Sánchez Pérez, E. A. Non-additive measures Measures of information Choquet integral Fuzzy measure Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal necessary conditions on Λ are required, several -spaces of integrable functions associated to Λ appear in such a way that the integration map can be defined in them. We study the properties of these spaces and how they are related. We show that the behavior of the -spaces and the integration map can be improved in the case when X is an order continuous Banach lattice, providing new tools for (non-linear) operator theory and information sciences. Ministerio de Economía y Competitividad MTM2015-65888-C4-1-P Ministerio de Economía y Competitividad MTM2016-77054-C2-1-P Junta de Andalucía FQM-7276 Elsevier https://hdl.handle.net/11441/103812 https://doi.org/10.1016/j.fss.2017.05.014 |
| spellingShingle | Choquet type L1-spaces of a vector capacity Delgado Garrido, Olvido Non-additive measures Measures of information Choquet integral Fuzzy measure |
| status_str | submittedVersion |
| title | Choquet type L1-spaces of a vector capacity |
| title_full | Choquet type L1-spaces of a vector capacity |
| title_fullStr | Choquet type L1-spaces of a vector capacity |
| title_full_unstemmed | Choquet type L1-spaces of a vector capacity |
| title_short | Choquet type L1-spaces of a vector capacity |
| title_sort | Choquet type L1-spaces of a vector capacity |
| topic | Non-additive measures Measures of information Choquet integral Fuzzy measure |
| topic_facet | Non-additive measures Measures of information Choquet integral Fuzzy measure |
| url | https://hdl.handle.net/11441/103812 https://doi.org/10.1016/j.fss.2017.05.014 |