Notions of Probabilistic Computability on Represented Spaces
Дата
Авторы
Bosserhoff,Volker
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
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.
Ключевые слова
computable analysis , computable measures , probabilistic computation