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On the Kurzweil integral for functions with values in ordered spaces. II. (English) Zbl 0821.28007

The authors prove, for the integral defined in Part I by B. Riečan [Acta Math. Univ. Comenianae 56/57, 75-83 (1990; Zbl 0735.28008)], the usual theorem on the integral of bounded limits of uniformly convergent sequences.

MSC:

28B15 Set functions, measures and integrals with values in ordered spaces
26A39 Denjoy and Perron integrals, other special integrals

Citations:

Zbl 0735.28008
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References:

[1] FREMLIN D. H.: A direct proof of the Matthes-Wright integral extension theorem. J. London Math. Soc. 11 (1975), 276-284. · Zbl 0313.06016
[2] KURZWEIL J.: Nicht absolut Konvergente Integrate. Teubner, Leipzig, 1980.
[3] LUXEMBURG W. A., ZAANEN A. C.: Riesz Spaces. North-Holland, Amsterdam, 1971. · Zbl 0231.46014
[4] MALIČKÝ P.: The monotone limit convergence theorem for elementary functions with values in a vector lattice. Comment. Math. Univ. Carolin. 27 (1986), 53-67. · Zbl 0608.28004
[5] RIEČAN B.: On the Kurzweil integral for functions with values in ordered spaces I. Acta Math. Univ. Comenian. 56-57 (1990), 75-83. · Zbl 0735.28008
[6] RIEČAN B.: On the Kurzweil integral in Compact Topological Spaces. Rad. Mat. 2 (1986), 151-163. · Zbl 0623.28003
[7] RIEČAN B., VOLAUF P.: On a technical lemma in lattice ordered groups. Acta Math. Univ. Comenian. 44-45 (1984), 31-35. · Zbl 0558.06019
[8] WRIGHT J. D. M.: The measure extension problem for vector lattices. Ann. Inst. Fourier (Grenoble) 21 (1971), 65-85. · Zbl 0215.48101
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