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

Maličký, Peter

Commentat. Math. Univ. Carol. 27, 53-67 (1986).

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

Keywords:

integration theory of functions with values in a vector lattice; monotone limit convergence theorem; Daniell integration

Citations:

Zbl 0215.48101