Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes. (English) Zbl 1349.46044
Summary: A Vitali-type theorem for vector lattice-valued modulars with respect to filter convergence is proved. Some applications are given to modular convergence theorems for moment operators in the vector lattice setting, and also for the Brownian motion and related stochastic processes.
MSC:
| 46G10 | Vector-valued measures and integration |
| 41A35 | Approximation by operators (in particular, by integral operators) |
| 46G12 | Measures and integration on abstract linear spaces |
| 47G10 | Integral operators |
| 60G15 | Gaussian processes |
Keywords:
vector lattice; filter convergence; modular; Vitali convergence theorem; Brownian motion; moment operator; Itô integralReferences:
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