Algebraic ramifications of the common extension problem for group-valued measures
Göbel, Rüdiger ; Shortt, R.
Fundamenta Mathematicae, Tome 144 (1994), p. 1-20 / Harvested from The Polish Digital Mathematics Library
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Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:212048 
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     title = {Algebraic ramifications of the common extension problem for group-valued measures},
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     volume = {144},
     year = {1994},
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     zbl = {0851.28007},
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Göbel, Rüdiger; Shortt, R. Algebraic ramifications of the common extension problem for group-valued measures. Fundamenta Mathematicae, Tome 144 (1994) pp. 1-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p1bwm/

[00000] [1] A. Basile and K. P. S. Bhaskara Rao, Common extensions of group-valued charges, Boll. Un. Mat. Ital. 7 (5-A) (1991), 157-162. | Zbl 0741.28008

[00001] [2] A. Basile, K. P. S. Bhaskara Rao and R. M. Shortt, Bounded common extensions of bounded charges, Proc. Amer. Math. Soc. 121 (1994), 137-143. | Zbl 0807.28002

[00002] [3] K. P. S. Bhaskara Rao and R. M. Shortt, Common extensions for homomorphisms and group-valued charges, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 125-140. | Zbl 0777.28005

[00003] [4] K. P. S. Bhaskara Rao and R. M. Shortt, Group-valued charges: common extensions and the finite Chinese remainder property, Proc. Amer. Math. Soc. 113 (1991), 965-972. | Zbl 0743.28004

[00004] [5] T. Carlson and K. Prikry, Ranges of signed measures, Period. Math. Hungar. 13 (1982), 151-155. | Zbl 0523.28003

[00005] [6] S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235. | Zbl 0138.01801

[00006] [7] L. Fuchs, Infinite Abelian Groups, Vols. I and II, Academic Press, New York, 1970 & 1973.

[00007] [8] R. Göbel and R. Prelle, Solution of two problems on cotorsion abelian groups, Arch. Math. (Basel) 31 (1978), 423-431. | Zbl 0387.20040

[00008] [9] Z. Lipecki, On common extensions of two quasi-measures, Czechoslovak Math. J. 36 (1986), 489-494. | Zbl 0622.28007

[00009] [10] E. Marczewski, Measures in almost independent fields, Fund. Math. 38 (1951), 217-229. | Zbl 0045.02303

[00010] [11] K. M. Rangaswamy and J. D. Reid, Common extensions of finitely additive measures and a characterization of cotorsion Abelian groups, in: Proc. Curacao, Abelian Groups, Marcel Dekker, New York, 1993, 231-238. | Zbl 0817.20056

[00011] [12] L. Salce, Cotorsion theories for abelian groups, Symposia Math. 23 (1979), 11-32.