The induced capacity and Choquet integral monotone convergece
| dc.creator | Teper, Roee | |
| dc.date | 2007-11-15 | |
| dc.date.accessioned | 2026-07-07T08:43:05Z | |
| dc.date.available | 2026-07-07T08:43:05Z | |
| dc.description | Given a probability measure over a state space, a partial collection (sub-$σ$-algebra) of events whose probabilities are known, induces a capacity over the collection of all possible events. The \emph{induced capacity} of an event $F$ is the probability of the maximal (with respect to inclusion) event contained in $F$ whose probability is known. The Choquet integral with respect to the induced capacity coincides with the integral with respect to a \emph{probability specified on a sub-algebra} (Lehrer \cite{Lehrer2}). We study Choquet integral monotone convergence and apply the results to the integral with respect to the induced capacity. The paper characterizes the properties of sub-$σ$-algebras and of induced capacities which yield integral monotone convergence. | |
| dc.identifier | https://arxiv.org/abs/0711.2375 | |
| dc.identifier | http://arxiv.org/abs/0711.2375 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142192 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | The induced capacity and Choquet integral monotone convergece | |
| dc.type | text |