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: | ; |
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| 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 |
| Summary: | 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. |
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