Algebraic ramifications of the common extension problem for group-valued measures

Rüdiger Göbel; R. Shortt

Fundamenta Mathematicae (1994)

  • Volume: 146, Issue: 1, page 1-20
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Göbel, Rüdiger, and Shortt, R.. "Algebraic ramifications of the common extension problem for group-valued measures." Fundamenta Mathematicae 146.1 (1994): 1-20. <http://eudml.org/doc/212048>.

@article{Göbel1994,
abstract = {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.},
author = {Göbel, Rüdiger, Shortt, R.},
journal = {Fundamenta Mathematicae},
keywords = {field of sets; Stone space; charge; common extension; Abelian group; independence},
language = {eng},
number = {1},
pages = {1-20},
title = {Algebraic ramifications of the common extension problem for group-valued measures},
url = {http://eudml.org/doc/212048},
volume = {146},
year = {1994},
}

TY - JOUR
AU - Göbel, Rüdiger
AU - Shortt, R.
TI - Algebraic ramifications of the common extension problem for group-valued measures
JO - Fundamenta Mathematicae
PY - 1994
VL - 146
IS - 1
SP - 1
EP - 20
AB - 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.
LA - eng
KW - field of sets; Stone space; charge; common extension; Abelian group; independence
UR - http://eudml.org/doc/212048
ER -

References

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  1. [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. Zbl0741.28008
  2. [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. Zbl0807.28002
  3. [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. Zbl0777.28005
  4. [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. Zbl0743.28004
  5. [5] T. Carlson and K. Prikry, Ranges of signed measures, Period. Math. Hungar. 13 (1982), 151-155. Zbl0523.28003
  6. [6] S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235. Zbl0138.01801
  7. [7] L. Fuchs, Infinite Abelian Groups, Vols. I and II, Academic Press, New York, 1970 & 1973. 
  8. [8] R. Göbel and R. Prelle, Solution of two problems on cotorsion abelian groups, Arch. Math. (Basel) 31 (1978), 423-431. Zbl0387.20040
  9. [9] Z. Lipecki, On common extensions of two quasi-measures, Czechoslovak Math. J. 36 (1986), 489-494. Zbl0622.28007
  10. [10] E. Marczewski, Measures in almost independent fields, Fund. Math. 38 (1951), 217-229. Zbl0045.02303
  11. [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. Zbl0817.20056
  12. [12] L. Salce, Cotorsion theories for abelian groups, Symposia Math. 23 (1979), 11-32. 

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