Notions of Probabilistic Computability on Represented Spaces
| dc.creator | Bosserhoff,Volker | |
| dc.date | 2008 | |
| dc.date.accessioned | 2024-02-06T12:56:22Z | |
| dc.date.available | 2024-02-06T12:56:22Z | |
| dc.description | We define and compare several probabilistic notions of computability for mappings from represented spaces (that are equipped with a measure or outer measure) into computable metric spaces. We thereby generalize definitions by [Ko 1991] and Parker (see [Parker 2003, Parker 2005, Parker 2006]), and furthermore introduce the new notion of computability in the mean. Some results employ a notion of computable measure that originates in definitions by [Weihrauch 1999] and [Schröder 2007]. In the spirit of the well-known Representation Theorem (see [Weihrauch 2000]), we establish dependencies between the probabilistic computability notions and classical properties of mappings. We furthermore present various results on the computability of vector-valued integration, composition of mappings, and images of measures. Finally, we discuss certain measurability issues arising in connection with our definitions. | |
| dc.format | text/html | |
| dc.identifier | https://doi.org/10.3217/jucs-014-06-0956 | |
| dc.identifier | https://lib.jucs.org/article/29014/ | |
| dc.identifier.uri | https://openrepository.mephi.ru/handle/123456789/9671 | |
| dc.language | en | |
| dc.publisher | Journal of Universal Computer Science | |
| dc.relation | info:eu-repo/semantics/altIdentifier/eissn/0948-6968 | |
| dc.relation | info:eu-repo/semantics/altIdentifier/pissn/0948-695X | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | J.UCS License | |
| dc.source | JUCS - Journal of Universal Computer Science 14(6): 956-995 | |
| dc.subject | computable analysis | |
| dc.subject | computable measures | |
| dc.subject | probabilistic computation | |
| dc.title | Notions of Probabilistic Computability on Represented Spaces | |
| dc.type | Research Article |