## The monotone limit convergence theorem for elementary functions with values in a vector lattice.(English)Zbl 0608.28004

If $$Y$$ is a vector lattice (of a certain type), then there is a good Daniell integration theory for $$Y$$-valued functions [J. D. M. Wright, Ann. Inst. Fourier 21 (1971), No. 4, 65–85 (1971; Zbl 0215.48101)]. Of course, in the case of a probability space $$(X,S,m)$$ it is not known whether the assumptions of the Daniell integration scheme are satisfied for $$Y$$-valued simple m-integrable functions. The author gives a necessary and sufficient condition for it.
Reviewer: B.Riečan

### MSC:

 28B15 Set functions, measures and integrals with values in ordered spaces

Zbl 0215.48101
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