Capek, Peter Decomposition theorems in measure theory. (English) Zbl 0452.28002 Math. Slovaca 31, 53-69 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 6 Documents MSC: 28A12 Contents, measures, outer measures, capacities 28B10 Group- or semigroup-valued set functions, measures and integrals Keywords:Lebesgue decomposition theorem; Hahn decomposition theorem; Hahn-Herer theorem; measures with values in a partially ordered topological semigroup PDF BibTeX XML Cite \textit{P. Capek}, Math. Slovaca 31, 53--69 (1981; Zbl 0452.28002) Full Text: EuDML OpenURL References: [1] NEUBRUNN T.: Замєчаниє об абсолютной нєпрєрывности мєр. Russian Mat-fyz. Čas 16 1966, 21-30. [2] NEUBRUNN T.: On the equivalence of an exhaustion principle and the axiom of choìce. Fund. Math 60, 1967, 209-211. · Zbl 0169.38301 [3] BERBERIAN D. K.: Measure and integration. New York 1960. · Zbl 0126.08001 [4] BROOKS S. K.: The Lebesgue decomposition theorem for measures. The Amer. Math. Month. 78, N. 6, 1971, 660-662. · Zbl 0214.07101 [5] CAPEK P.: Theorèmes de decomposition en theorie de la mesure I, II. Publications du Semin. d’Analyse de Brest, juin 1976. [6] CAPEK P.: Théorèmes de décomposition en theorie de la measure. R.A.S.P. t 25, 1967, Serie A-537 [7] ČERVEŇANSKY J., DRAVECKY J.: A note on Hahn decomposition. Acta F.R.N. Univ. Comen.- Mathematica XXV - 1971, 27-29. · Zbl 0228.28002 [8] FICKER V.: Dominated classes and related questions. Acta F.R.N. Univ. Comen.- Mathematica X, 7, 1966, 3-18. · Zbl 0143.27301 [9] FICKER V.: An abstract formulation of the Lebesgue decomposition theorem. Aust. Math. Soc. 12, 1971, 101-105. · Zbl 0203.35901 [10] FICKER V.: On the equivalence of a countable disjoint class of sets of positive measure and a weaker condition than total \(\sigma\)-finiteness of measures. Bull. Austral. Math. Soc. 1 1979, 237-243. · Zbl 0174.09103 [11] FUCHS L.: Partially ordered algebraic system. Pergamon Press 1963. · Zbl 0137.02001 [12] HAHN H., ROSENTHAL A.: Set functions. The University of New Mexico Press 1948. · Zbl 0033.05301 [13] HALMOS P. R.: Measure theory. Van Nonstrand-New York 1950. · Zbl 0040.16802 [14] HERER. W.: Decomposition of measures with values in a topological group. Bull. de ľAcad Polon. des Sciences Série Math. Astron. et Phys. 20, 1972, 203-205. · Zbl 0244.28006 [15] HOFFMANN-J\?RGENSEN J.: Vector measures. Math. Scand. 28, 1971, 5-32. · Zbl 0217.38001 [16] KLUVÁNEK I.: К тєории вєкторныцх мєр. Mat.-fyz. Čas. 11, 3, 1961. [17] LIPECKI Z.: A characterization of group-valued measures satisfying the countable chain condition. Coll. Math. 31, 1974, 231-234. · Zbl 0271.28009 [18] LIPECKI Z.: Decomposition theorems for Boolean rings, with applications to semigroup-valued measures. Commentationes Mathematicae. XX, 1978, 397-403. · Zbl 0372.28015 [19] MUSIAL K.: Absolute continuity of vector measures. Coll. Math. 27, 1973, 319-321. · Zbl 0262.46049 [20] MUSIAL K.: Absolute continuity and the range of group valued Vmeasures. Bull. Acad. Polon. Sci. Série Sci., Math., Astr. et Phys. 21, 1973, 105-113. · Zbl 0253.28003 [21] TRAYNOR T.: Decomposition of group-valued additive set functions. Ann. Inst. Fourier, Grenoble, 22, 3, 1972, 131-140. · Zbl 0228.28004 [22] YAM TING WOO J.: An elementary proof of the Lebesgue decomposition theorem. The Amer. Math. Monthly 78, 7, 1971, p. 783. · Zbl 0222.28004 [23] DOBRAKOV I.: On submeasures I. Dissertationes Mathemat. CXII, 1974. · Zbl 0292.28001 [24] Mme GODET-THOBIE C.: Multimesures et Multimesures de Transitions. Thèse. Montpellier. 1975. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.