Document Zbl 0482.28018

Integration in partially ordered linear spaces. (English) Zbl 0482.28018

Math. Slovaca 31, 39-51 (1981).

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MSC:

28B15	Set functions, measures and integrals with values in ordered spaces
28B05	Vector-valued set functions, measures and integrals
46G10	Vector-valued measures and integration

Keywords:

strong integrals; functions with values in ordered vector spaces; weak integral of the Pettis type; Daniell procedure; monotone convergence theorems

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References:

[1]	CHOQUET G.: Lectures on Analysis, VI. W. A. Benjamin, INC. 1969. · Zbl 0181.39602
[2]	FREMLIN D. H.: A direct proof of the Mathes-Wright integral extension theorem. J. London M.S., 11, 1975, 276-284. · Zbl 0313.06016 · doi:10.1112/jlms/s2-11.3.276
[3]	LUXEMBURG W. A., ZAANEN A. C.: Riesz spaces 1. Amsterdam 1971. · Zbl 0231.46014
[4]	JAMESON G.: Ordered Linear Spaces. Berlin 1970. · Zbl 0196.13401 · doi:10.1007/BFb0059130
[5]	POTOCKÝ R.: On random variables having values in a vector lattice. Math. Slovaca 27, 1977, 267-276. · Zbl 0372.28012
[6]	RIEČAN B.: O prodolženii operatorov s značeniami v linejnich poluuporiadočennych prostranstvách. Čas. Pěst. Mat., 93, 1968, 459-471.
[7]	SEMADENI Z.: Banach Spaces of Continuous Functions. Warszawa. · Zbl 0478.46014 · doi:10.1007/BFb0094629
[8]	SIKORSKI R.: Funkcje rzeczywiste. Warszawa, 1958. · Zbl 0093.05603
[9]	VOLAUF P.: On extension of maps with values in ordered space. Math. Slov. 30, 1980, 351-361. · Zbl 0448.28007
[10]	VONKOMEROVÁ M.: Extension of operators. Math. Slov. 30, 1980, 351-361.
[11]	WRIGHT J. D. M.: The measure extension problem for vector lattices. Ann. Inst. Fourier (Grenoble) 21 Fasc. 4 (1971) 65-85. · Zbl 0215.48101 · doi:10.5802/aif.393

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