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On compact group-valued measures. (English) Zbl 0911.28010
Summary: Various concepts of compactness for partially ordered group-valued measures are investigated. Relations between different types of regularities in partially ordered groups are discussed; in the main results the lattice structure of po-groups is not assumed.
##### MSC:
 28B15 Set functions, measures and integrals with values in ordered spaces 28B10 Group- or semigroup-valued set functions, measures and integrals
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##### References:
 [1] BERNAU S. J.: Unique representation of Archimedean lattice groups and normal Archimedean lattice rings. Proc. London Math. Soc. (3) 15 (1965), 599-631. · Zbl 0134.10802 [2] BIRKHOFF G.: Lattice Theory. Amer. Math. Soc, Providence, R. I.-1967. · Zbl 0153.02501 [3] FREMLIN D. H.: A direct proof of the Mathes-Wright integral extension theorem. J. London Math. Soc. (2) 11 (1975), 276-284. · Zbl 0313.06016 [4] HRACHOVINA E.: A generalization of the Kolmogorov consistency theorem for vector measures. Acta Math. Univ. Comenian. 54-55 (1988), 141-145. · Zbl 0723.28004 [5] JAMESON G.: Ordered Linear Spaces. Lecture Notes in Math. 141, Springer, Berlin-New York, 1970. · Zbl 0196.13401 [6] LUXEMBURG W. A.-ZAANEN A. C.: Riesz Spaces I. North Holland, Amsterdam, 1971. · Zbl 0231.46014 [7] MARCZEWSKI E.: On compact measures. Fund. Math. 40 (1953), 113-124. · Zbl 0052.04902 [8] RIEČAN B.: On the lattice group valued measures. Časopis Pěst. Mat. 101 (1976), 343-349. [9] RIEČAN B.: Notes on lattice-valued measures. Acta Math. Univ. Comenian. XLII-XLIII (1983), 181-192. · Zbl 0568.28010 [10] RIEČAN B.: On measures and integrals with values in ordered groups. Math. Slovaca 33 (1983), 153-163. · Zbl 0519.28004 [11] RIEČAN J.: On the Kolmogorov consistency theorem for Riesz space valued measures. Acta Math. Univ. Comenian. 48-49 (1986), 173-180. · Zbl 0626.60007 [12] ŠIPOŠ J.: On extension of group valued measures. Math. Slovaca 40 (1990), 279-286. · Zbl 0760.28007 [13] VOLAUF P.: On extension of maps with values in ordered spaces. Math. Slovaca 30, (1980), 351-361. · Zbl 0448.28007 [14] VOLAUF P.: On various notions of regularity in ordered spaces. Math. Slovaca 35 (1985).127-130. · Zbl 0597.28017 [15] VOLAUF P.: On the lattice group valued submeasures. Math. Slovaca 40 (1990). 107-411. · Zbl 0760.28008 [16] VOLAUF P.: Alexandrov and Kolmogorov consistency theorem for measures with values in partially ordered groups. Tatra Moutains Math. Publ. 3 (1993), 237-244. · Zbl 0820.28006 [17] WRIGHT J. D. M.: The measure extension problem for vector lattices. Ann. Inst. Fourier (Grenoble) 21 (1971), 65-85. · Zbl 0215.48101 [18] WRIGHT J. D. M.: An algebraic characterization of vector lattices with the Borel regularity property. J. London Math. Soc. (2) 7 (1973), 277-285. · Zbl 0266.46036 [19] WRIGHT J. D. M.: Measures with values in partially ordered spaces: regularity and $$\sigma$$-additivity. Measure Theory. Lecture Notes in Math. 541 (D. Kozlov, A. Bellow. Springer, Berlin-New York, 1976, pp. 267-276. · Zbl 0357.28011 [20] WRIGHT J. D. M.: Sur certain espaces vectoriels reticules. C.R. Acad. Sc. Paris 290 (1990), 169-170. · Zbl 0427.46012
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