Abstract
For Archimedean vector lattices X, Y and the positive cone \({\mathbb{L}}\) of all regular linear operators L : X → Y, a theory of sequential convergences of functions connected with an \({\mathbb{L}}\) -valued measure is introduced and investigated.
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Haluška, J., Hutník, O. On convergences of measurable functions in Archimedean vector lattices. Positivity 14, 515–527 (2010). https://doi.org/10.1007/s11117-009-0034-3
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DOI: https://doi.org/10.1007/s11117-009-0034-3
Keywords
- Archimedean vector lattices
- Operator valued measure
- (r)-Convergence
- Convergence in measure
- Almost everywhere convergence
- Almost uniform convergence
- Egoroff theorem